Lesson on the topic: “Fundamentals of logic. Algebra of statements".

Lesson Objectives: introduce children to forms of thinking, form concepts: logical statement, logical quantities, logical operations; create conditions for the development of students’ cognitive interest, promote the development of memory, attention, and logical thinking; promote the ability to listen to the opinions of others and work in a team.

During the classes.

I.Communicate the topic and objectives of the lesson.

How does a person think? What in our speech is a statement and what is not? What are the similarities and differences in arithmetic multiplication and logical multiplication, let's get acquainted with the basic logical expressions and operations, and learn some components of our thinking.

II. Explanation of new material.

1. Modern logic is based on teachings created by ancient Greek thinkers, although the first teachings about the forms and methods of thinking arose in Ancient China and India. The founder of formal logic is Aristotle, who was the first to separate the logical forms of thinking from its content.

Logics- it is the science of forms and ways of thinking. This is the study of methods of reasoning and evidence. We learn the laws of the world, the essence of objects, and what they have in common through abstract thinking. Thinking is always carried out through concepts, statements and conclusions.

Concept- This is a form of thinking that identifies the essential features of an object or class of objects, allowing them to be distinguished from others. Example: rectangle, pouring rain, computer.

Statement- this is the formulation of your understanding of the world around you. A statement is a declarative sentence in which something is affirmed or denied.

A statement can be told whether it is true or false. A statement in which the connection of concepts correctly reflects the properties and relationships of real things will be true. A statement will be false if it contradicts reality.

Example: true statement: “The letter “a” is a vowel”, false statement: “The computer was invented in the middle of the 19th century.”

Example: Which of the sentences are statements? Determine their truth.

1.How long is this tape? 2.Listen to the message.

3. Do morning exercises! 4.Name the information input device.

5. Who is missing? 6.Paris is the capital of England. (LIE)

7. The number 11 is prime. (TRUE) 8. 4 + 5=10. (LIE)

9. You can’t even pull a fish out of a pond without difficulty. 10. Add the numbers 2 and 5.

11.Some bears live in the north. (TRUE) 12. All bears are brown. (LIE)

13.What is the distance from Moscow to Leningrad?
Inference- this is a form of thinking with the help of which a new judgment (knowledge or conclusion) can be obtained from one or more judgments.

2. Logical expressions and operations

Algebra is the science of general operations, similar to addition and multiplication, that are performed not only on numbers, but also on other mathematical objects, including statements. This algebra is called algebra of logic. The algebra of logic is abstracted from the semantic content of statements and takes into account only the truth or falsity of a statement.

You can define the concepts of logical variable, logical function and logical operation.

Boolean variable- This is a simple statement containing only one thought. Its symbolic designation is a Latin letter. The value of a logical variable can only be the constants TRUE and FALSE (1 and 0).

Compound statement - logical function, which contains several simple thoughts connected to each other using logical operations. Its symbolic designation is F(A,B,...). Based on simple statements, compound statements can be constructed.

Logical operations- logical action.

There are three basic logical operations - conjunction, disjunction and negation and additional ones - implication and equivalence.

In the algebra of logic, statements are denoted names of logical variables (A, B, C), which can take the values ​​true (1) or false (0). Truth, lies - logical constants.
Boolean expression- simple or complex statement. A complex statement is constructed from simple ones using logical operations.

Logical operations.

Conjunction (logical multiplication)– connecting two logical expressions (statements) using the conjunction AND. This operation is denoted by the symbols & and ∧.

Conclusion: The logical operation of conjunction is true only if both simple statements are true, otherwise it is false.

Conclusion: The logical operation disjunction is false if both simple statements are false. In other cases it is true

Conclusion: if the original expression is true, then the result of its negation will be false, and vice versa, if the original expression is false, then it will be true.

AB is equivalentVIN. Prove.

Logical equality (equivalence): if and only if...; signs , . Truth table:

AB is equivalent to (AV ) & ( VB) or (&)V (A& B).

Prove 1st algebraically on the board. Prove 2nd using spreadsheets yourself.

Sequence of operations:
negation, conjunction, disjunction, implication, equivalence . In addition, the order in which an operation is performed is affected by parentheses that can be used in Boolean formulas.

III. Consolidation of the studied material.

Example 1. From two simple statements, construct a complex statement using the logical operations AND, OR.

All students study mathematics. All students study literature.

All students study mathematics and literature.

The blue cube is smaller than the red one. Blue is less than green.

There are textbooks in the office. There are reference books in the office.

Example 2. Calculate the value of a logical formula: not X and Y or X and Z, if the logical variables have the following values: X=0, Y=1, Z=1
Solution. Let us mark with numbers above the order of operations in the expression:
1. not 0=1
2. 1 and 1= 1
3. 0 and 1 =0
4. 1 or 0 =1 answer: 1

Example 3. Determine the truth of the formula not P or Q and not P

Example 4. Write down the following statement in the form of a logical expression: “In the summer, Petya will go to the village and, if the weather is good, he will go fishing.”

1. Let’s break the compound statement into simple statements: “Petya will go to the village,” “The weather will be good,” “He will go fishing.”

Let's denote them through logical variables: A = Petya will go to the village; B = The weather will be good; C = He will go fishing.

2. Let's write the statement in the form of a logical expression, taking into account the order of actions. If necessary, place brackets: F = A& (B+C).

Example 5..Write the following statements as logical expressions.

1.The number 17 is odd and two-digit.

2. It is not true that a cow is a predatory animal.

Example 6. Compose and write true complex statements from simple ones using logical operations.

1. It is not true that 10Y5 and Z(answer:(Y 5) & (Z

2.Z is min(Z,Y) (answer: Z

3.A is max(A,B,C) (answer: (AB)&(AC)).

4. Any of the numbers X,Y,Z is positive (answer: (X0)v(Y0)v(Z0).

5. Any of the numbers X,Y,Z is negative (answer: (X

6. At least one of the numbers K,L,M is not negative (answer: (K 0) v (I 0) v(M O))

7. At least one of the numbers X,Y,Z is not less than 12 (answer: (X 12) v(Y 12) v (Z 12))

8. All numbers X,Y,Z are equal to 12 (answer: (X=12)&(Y=12)&(Z=12)).

9.If X is divisible by 9, then X is divisible by 3 ((X is divisible by 9)→(X is divisible by 3)).

10. If X is divisible by 2, then it is even ((X is divisible by 2)→(X is even)).

IV. Summing up the lesson, in grading.

V.Homework learn basic definitions from a notebook, know the notation.

Municipal educational institution
secondary school No. 1
named after the 50th anniversary of "Krasnoyarskgesstroy"

Sayanogorsk 2009

Municipal stage of the republican competition
"Electronic developments" in 2009

Direction: natural science

Title of the competition work

Logical operations

computer science lesson in 9th grade

IT-teacher,
1 qualification category

Technological lesson map

Teacher's name

Oreshina Nina Semenovna

Municipal educational institution secondary school No. 1 named after the 50th anniversary of “Krasnoyarskgesstroy”, Sayanogorsk

Subject, class

Computer Science, 9th grade

Lesson topic,

"Logical operations"

Lesson type

Combined lesson

The purpose of the lesson

Lesson Objectives

educational

developing

educational

1. Develop logical thinking.

Type of ICT tools used in the lesson (universal, OER on CD-ROM, Internet resources)

Power Point presentation;

Text Document

Required Hardware and Software

• Multimedia projector;

Literature

Computer Science and ICT. Textbook. 8–9 grades / Edited by prof. N.V. Makarova. – St. Petersburg: Peter, 2007

Program in computer science and ICT (system information concept) for a set of textbooks on computer science and ICT grades 5-11, 2007

Informatics and ICT: A manual for teachers. Part 3. Technical support of information technologies / Edited by prof. N.V. Makarova. – St. Petersburg: Peter, 2008

ORGANIZATIONAL STRUCTURE OF THE LESSON

STAGE 1

Organizational

Updating students' attention to the lesson

Duration of the stage

Perception of the purpose of the lesson, mood for the lesson

Set students up for the lesson, concentrate students’ attention on the topic of the lesson.

STAGE 2

Updating knowledge

Updating students' knowledge

Duration of the stage

Work on tasks on cards.

Verification is carried out by demonstrating a presentation (2).

Form of organization of student activities

Task 1 – work on options on cards

Task 2 – individual work on multi-level tasks on cards

Functions of the teacher at this stage

organizing

Intermediate control

selective

STAGE 3

Learning new material

Introduce students to the simplest logical operations and stages of constructing a truth table

Duration of the stage

Main activity with ICT tools

Presentation demonstration (3-26 slides)

Form of organization of student activities

Individual,

Functions of the teacher at this stage

Presentation of new material

STAGE 4

Physical education minute.

Relieving local fatigue.

Duration of the stage

STAGE 5

Consolidation of new knowledge

Check your understanding of new material

Duration of the stage

Main activity with ICT tools

Presentation demonstration (27 - 32 slides)

Form of organization of student activities

Independent work of students in notebooks

Functions of the teacher at this stage

Organizing, consulting

Intermediate control

Self-control

STAGE 6

Summarizing. Reflection

Summarize the students’ knowledge acquired in the lesson

Duration of the stage

Form of organization of student activities

Reflexive comprehension

Functions of the teacher at this stage

organizing

Final control

Assessment of each student

STAGE 7

Homework

Consolidating knowledge acquired in class

Duration of the stage

Main activity with ICT tools

Presentation demonstration (33 slide)

Form of organization of student activities

individual

Functions of the teacher at this stage

consulting, guiding

Lesson outline

Item:"Informatics and ICT"

Class: 9

Lesson topic:“Logical operations” (1 lesson 80 minutes)

Goals:

Forming an understanding of propositional algebra and basic logical operations, familiarization with the algorithm for constructing truth tables.

Tasks:

During the lesson, ensure the assimilation and initial consolidation of new concepts.

Develop logical thinking

Develop the ability to identify essential features and properties.

Build communication skills.

Foster a work culture in the process of performing written work.

Means of education:

PC;MS Power Point;

Multimedia projector;Printer.

Computer Science and ICT. Textbook. 8–9 grades / Edited by prof. N.V. Makarova. – St. Petersburg: Peter, 2007.

Program in computer science and ICT (system information concept) for a set of textbooks on computer science and ICT for grades 5-11, 2007.

Informatics and ICT: A manual for teachers. Part 3. Technical support of information technologies / Edited by prof. N.V. Makarova. – St. Petersburg: Peter, 2008.

Lesson steps

1. Organizing time. Setting the lesson goal. 3 min.

   Updating knowledge (working with cards). 10 min.

   Explanation of new material. 37 min.

   Physical education minute. 3 min.

   Consolidation of new knowledge. 17 min.

   Summarizing. Reflection. 7 min.

   Setting homework. 3 min.

During the classes

1. Organizing time

Communicating the topic and setting lesson goals

Hello guys!

Today we will continue to study the elements of mathematical logic. The purpose of our lesson is to get acquainted with the basic logical operations and learn how to build truth tables for logical statements. At the end of the lesson, you will complete practice assignments that will help you evaluate how you have learned the new material. I hope for mutual understanding and coherence in work.

1. Updating knowledge

Working with cards

Next, we monitor knowledge on the topic “Basic concepts of logical algebra.” Working in pairs according to the options, students write down their answers on a sheet of paper, which is previously distributed by the teacher. After completing the tasks, there is a test in pairs with an assessment. The correct answers are shown in the presentation frames.

Sample for option 1.

Option 1.

In formal logic concept called

B) a form of thinking that reflects the distinctive essential features of objects or phenomena.

C) a form of thinking that affirms or denies something about objects, their properties or relationships between them.

A) A- River;

B) A- Schoolchildren;

B- Athletes.

B) A- Dairy product;

B- Sour cream.

A) The number 6 is even.

B) Look at the board.

C) Some bears are brown.

Determine the type of statement.

A) Paris is the capital of China.

B) Some people are artists.

C) The tiger is a predatory animal.

Which of the following statements are common?

Not all books contain useful information.

The cat is a pet.

All soldiers are brave.

No attentive person will make a mistake.

Some students are bad students.

All pineapples taste good.

My cat is a terrible bully.

Any unreasonable person walks on his hands.

Sample for option 2.

Option 2.

In formal logic statement called

A) a form of thinking with the help of which a new judgment (conclusion) can be obtained from one or more judgments (premises).

B) a form of thinking that reflects the distinctive essential features of objects or phenomena.

C) a form of thinking that affirms or denies something about objects, their properties or relationships between them.

This Euler-Venn diagram illustrates the relationships between the following scope of concepts:

A) A- River;

B) A- Geometric figure - rhombus;

B- Geometric figure - rectangle.

B) A- Dairy product;

B- Sour cream.

Which of the sentences are statements? Determine their truth.

A) Napoleon was the French emperor.

B) What is the distance from Earth to Mars?

B) Attention! Look to the right.

Determine the type of statement.

A) All robots are machines.

B) Kyiv is the capital of Ukraine.

C) Most cats love fish.

Which of the following statements are particular?

Some of my friends collect stamps.

All medicines taste bad.

Some medicines taste good.

A is the first letter in the alphabet.

Some bears are brown.

The tiger is a predatory animal.

Some snakes do not have poisonous teeth.

Many plants have healing properties.

All metals conduct heat.

The answer sheet might look like this:

1. Explanation of new material.

The objects of Boolean algebra are propositions. If statements are connected by logical operations, then they are usually called logical expressions .

In the algebra of logic, various operations can be performed on statements (just as in the algebra of numbers the operations of addition, multiplication, division, and exponentiation on numbers are defined). Using logical operations on simple statements, compound or complex statements are obtained. In natural language, compound statements are formed using conjunctions.

For example:

Logical operations are specified by truth tables and can be graphically illustrated using Euler-Venn diagrams.

Let's look at the basic logical operations.

Logical negation (inversion)

Logical negation formed from a statement by adding the particle “not” or using the figure of speech “ it is not true that…».

Logical negation – a one-place operation, since it involves one statement (one argument).

The operation is denoted by the particle NOT (NOT A), the sign: ¬A (¬A) or the line above the statement designation (Ā).

Example No. 1.

A= ( Aristotle the founder of logic.}

Ā= { It is not true that Aristotle is the founder of logic.}

Example No. 2.

A= ( Now there is a literature lesson.}

Ā= { It is not true that there is a literature lesson going on now.}

As a result of the negation operation, the logical meaning of the statement is reversed. The original expressions are usually called prerequisites .

The inversion of a statement is true when the statement is false, and false when the statement is true.

This can be displayed using a table:

Table 1.

The table with all possible values ​​of the initial expressions and the corresponding results of the operation is called truth tables .

If we designate False as 0 and True as 1, the table will look like this. As shown in the textbook on page 347.

Table 2. Truth table of logical negation operation

Mnemonic rule: The word “inversion” means that white changes to black, good to evil, beautiful to ugly, truth to lie, lie to truth, zero to one, one to zero.

Notes:

Logical addition (disjunction) is formed by combining two statements into one using the conjunction “or”. This is a two-place operation, since it involves two statements (two arguments). The operation is indicated by the union OR, the sign \/, and sometimes the sign + (logical addition).

In Russian, the conjunction “or” is used in a double sense.

For example, in the sentence Usually at 8 pm I watch TV or drink tea, the conjunction “or” is taken in a non-exclusive (unifying) sense, since you can only watch TV or only drink tea, but you can also drink tea and watch TV at the same time, because that your mother is not strict. This operation is called non-strict disjunction. (If my mother was strict, she would only allow me to watch TV, or only drink tea, but not combine eating with watching TV.)

In the statement This noun, whether plural or singular, the conjunction “or” is used in an exclusive (disjunctive) sense. This operation is called strict disjunction.

Determine the type of disjunction yourself:

Statement

Type of disjunction

Petya is sitting on the western or eastern stands of the stadium.

Strict

A student is traveling on a train or reading a book.

Lax

You will marry either Petya or Sasha.

Strict

Are you marrying Valya or Sveta?

Strict

Tomorrow it will rain or it won't.

Strict

Let's fight for purity. Cleanliness is achieved in this way: either do not litter, or clean often.

Lax

Teachers are either strict or not our kind.

Lax

In what follows we will consider only the non-strict disjunction. Designation: A IN.

The first sign of late blight disease is gray or brown spots on tomato leaves.

A= "There are gray spots on the leaves "

B= "Brown spots have appeared on the leaves"

C= "The plant is sick with late blight",

Judgment WITH=A /\ B.

A disjunction of two statements is false if and only if both statements are false, and true if at least one statement is true.

Table 3. Truth table of logical addition operation

A B

Mnemonic rule: disjunction is logical addition and it is easy to see that the equalities 0+0=0; 0+1=1; 1+0=1; true for ordinary addition, also true for the disjunction operation, but 11=1.

Logical multiplication (conjunction) is formed by combining two statements into one using the conjunction “ And" This is a two-place operation, since it involves two statements (two arguments). The operation is denoted by the union AND, the sign /\ or &, sometimes * (logical multiplication).

Designations: А·В; A^B; A&B.

A&B=(3+4=8 and 2+2=4)

The conjunction of two statements is true if and only if both statements are true, and false if at least one statement is false.

Table 4. Truth table of the logical multiplication operation.

A·/\B

note that in the truth table the values ​​of the incoming statements are written in ascending order.

Mnemonic rule: conjunction is logical multiplication, and we have no doubt that you noticed that the equalities 0 0 = 0; 0·1=0; 1·0=0; 1·1=1, true for ordinary multiplication, are also true for the conjunction operation.

A game

Teacher question: One wealthy man was afraid of robbers and ordered a lock that could be opened with two keys at the same time. What logical operation can the opening process be compared to?

Student answer: Logical multiplication. Each key alone does not open the lock. Only using two keys together allows it to be opened.

Teacher question: The boy Vasya was absent-minded and always lost his keys. As soon as the parents install a new lock, the old key is located (under the rug, in the pocket, in the briefcase). Come up with a “super lock” for Vasya so that the door cannot be opened by a stranger, but Vasya certainly can.

Student answer: A lock with a logical addition so that it can be opened by at least one key that is at hand.

note, that the logical addition operation is more “accommodating” (“at least something”), and the logical multiplication operation is more “strict” (“all or nothing”). If we take this fact into account, it will be easier to remember the signs of logical operations

The operations of inversion, conjunction and disjunction are basic logical operations . There are others (not the main ones), but they can be expressed through three main ones. As examples, consider the operations implications Andequivalence .

Logical consequence (implication) is formed by combining two statements into one using the figure of speech “ if….., then…..”

Designations: A→B, AB.

Example 1. A=(2·2=4) and B=(3·3=10).

AB=(If 2·2=4, then 3·3=10).

Example 2. If you learn the material, then you will pass the test (the statement is false only when the material is learned, but the test is not passed, because you can pass the test by accident, for example, if you came across the only familiar question or managed to use a cheat sheet).

Conclusion: An implication of two statements is false if and only if a false statement follows from a true statement.

Table 5. Truth table of the logical implication operation.

AB

Logical equality (equivalence)

Equivalence is formed by combining two statements into one using the figure of speech “…. then and only when…».

Equivalence designation: A=B; AB; A~B.

Example 1. A=(Right angle); B=(Angle is 90 0)

AB =(An angle is called right if and only if it is equal to 90 0 }

Example 2. When the sun shines on a winter day and the frost bites, it means that the atmospheric pressure is high.

Example 3. Statement A: “the sum of the digits that make up the number X, is divisible by 3", statement B: "X is divisible by 3." Operation A<=>B means the following: “a number is divisible by 3 if and only if the sum of its digits is divisible by 3.”

Conclusion: The equivalence of two statements is true if and only if both statements are true or both are false.

Table 6. Truth table of the logical equality operation.

AB

Compiling truth tables using a logical formula

More complex statements can be made from simple statements. These statements are similar to mathematical formulas. In addition to statements denoted by capital Latin letters and signs of logical operations, they may also contain brackets.

Operation priority:

inversion;

conjunction;

disjunction;

implication and equivalence.

Let's look at examples.

Example 1. Given the logical expression ¬A V B. It is required to construct a truth table.

Solution

¬ A

¬A V B

Example 2. The logical expression ¬A  B is given. It is required to construct a truth table.

Solution. A logical expression contains 2 statements A, B. This means that the truth table will contain 2 2 = 4 rows of possible combinations of the values ​​of the original statements A and B. The first two columns of the truth table will be filled with various combinations of argument values. Next will be the results of intermediate calculations and the final result.

¬ A

¬ A  B

Example 3. Given the logical expression ¬(A V B). It is required to construct a truth table.

Solution. A logical expression contains 2 statements A, B. This means that the truth table will contain 2 2 = 4 rows of possible combinations of the values ​​of the original statements A and B. The first two columns of the truth table will be filled with various combinations of argument values. Next will be the results of intermediate calculations and the final result.

A V B

¬(A V B)

1. Physical education minute

For the next job we need to focus. Let's do some exercises.

1. Consolidation of new knowledge.

To consolidate the material, perform the following tasks:

1. Below is a table, the left column of which contains the main logical conjunctions (connections), with the help of which complex statements are constructed in natural language. Fill in the right column of the table with the appropriate names of logical operations.

In natural language

In logic

…..It is not true that…..

*inversion

…..in that and only in that case….

equivalence

conjunction

conjunction

If…., then…..

*implication

……however….

conjunction

….if and only if….

equivalence

Or either…

*strict disjunction

….necessary and sufficient….

*equivalence

From ………it follows….

*implication

2. Formulate the negations of the following statements:

A) ( It is not true that New York City is the capital of the United States};

B) ( Kolya solved all 6 test tasks};

IN) ( It is false that the number 3 is not a divisor of the number 198}.

Solution:

A)(New York City is the capital of the USA };

B) ( It is not true that Kolya solved all 6 test tasks};

IN) ( The number 3 is not a divisor of 198}

Find the meanings of the expressions:

A) ((10)1)1; Solution: ((10)1)1=1;

Lesson #5

Subject: Logic and logical operations

The purpose of the lesson: IntroducestudentsWithmainconceptslogical operations . Contributeformationskillsdistinguishkindslogical operations , assimilationprincipledrawing uptablestruthForlogicaloperations.

Students should know What is logic, logical operations.

Students should be able to: perform operations on statements

During the classes

I . Organizing time

II . Checking homework

Working with the crossword puzzle “Translating numbers from one SS to another”

Learning new material

Logics

Logic (from the Greek logike) is the science of methods of proof.

Logics is the science of the forms and laws of human thinking, in particular, of methods of proof and refutation.

Statement- a declarative sentence in which something is affirmed or denied.

An example of simple statements: “All pines are trees.” If the statement is true, ittrue , and if it doesn’t match -false.

Statements are indicated by capital letters of the Latin alphabet.For example the meaning of the expression A = “All roses are flowers” ​​can be written as follows: A = 1. The meaning of the statement B = “All flies are birds”: B = 0. Statements can begeneral (when we are talking about a group of objects) orprivate. For example: “In any triangle, the sum of the angles is 180º” is a general statement. “There are black cats with white paws” - quotient.

Difficult is a statement consisting of simple ones connected by some kind of conjunction.

Logical operations

Logical operation - an operation on statements that allows you to compose new statements by combining simpler ones.

There are three basic logical operations - conjunction, disjunction and negation (inversion)

Conjunction(logical multiplication) is a two-place logical operation, corresponds to the union “AND”, otherwise called logical multiplication. Designated A&B or A˄B.

For example:

A- “Ducks winter in the south”

B- “Ducks spend their summer in the north”

S- “Ducks don’t fly”

А˄В˄С = “Ducks do not migrate, and winter in the south, and spend the summer in the north” - the result of the conjunction received a false statement.

Disjunction (logical addition) is a two-place logical operation, corresponds to the union “OR”, otherwise called logical addition. Designated A˅B.

For example:

A- “Today I’m expecting Petya to visit”

B- “Today I’m expecting Anya to visit”

We connect with the union “OR” and we get a complex statement - a logical sum

“Today I’m expecting Petya or Anya to visit” А˅В.

Negation (inversion) is a one-place logical operation, corresponds to the particle “NOT”, otherwise called logical negation. Denoted by ¬A, Ā.

For example:

Petya will be on duty - A.

Petya will not be on duty - Ā - denial.

A = “Six divided by two equals three” is a true statement

Ā= “Six divided by two does not equal three” - logical negation is false.

IV . Reinforcing the material learned

From simple statements, construct complex statements using the logical connectives “AND”, “OR” and determine their truth.

For example:

A- “All students study computer science”

B- “All students learn a foreign language”

А˄В = “All students study computer science and a foreign language”

Erbol is older than Madina. Salima is older than Madina

The red ball is larger than the green one. The red ball is larger than the yellow one.

Tomorrow it will snow. Tomorrow it will be cold.

Kairat is doing his homework. Kairat is watching football.

Aigul is having lunch. Aigul is learning a poem.

Indicate which statements are simple and which are complex.

Computer science lesson in progress

The number 3 is greater than the number 2.

I watched the play "True Friends"

Astana, Paris and Moscow are the capitals of the states.

Rain or sleet is expected tomorrow.

V. Lesson summary.

Grading homework

Homework

Write in your notebook without a negative sign: - (a).

Repeat the summary and retelling and learn the definitions of logical operations.

Lesson 3

Teacher:Asylbekova L. S. . Grade: 8 Date: ______________

Lesson topic: Logic and logical operations.

Lesson objectives:

1. form ideas: about basic logical functions (conjunction, disjunction, implication, equivalence, negation) and truth tables of logical functions; teach students to construct truth tables of logical functions.

2. develop independence when working with logical functions when constructing truth tables.

3. attentiveness, concentration, accuracy when constructing truth tables; responsibility and self-demandingness.

During the classes

Organizing time.

Call stage.

Students are asked to complete parts of the cluster on the topic “Logical functions. Truth tables of logical functions."

The teacher updates previously acquired knowledge, which will help more effective learning of the material through questions:

What is the keyword of our topic?

What is the principle of cluster levels?

What is on the first, second, third level?

What level are you having problems with?

What have you heard or already know about logical elements, implementing basic logical operations?

Fill out a table on the topic of the lesson.

Conception stage.

Summarize what is the purpose of our lesson today?

The teacher summarizes the students' statements with a demonstration of presentations. The purpose of the demonstration: to form an idea of ​​the truth table of a complex function, to consider the algorithm for compiling a truth table, to develop the ability to compile truth tables.

According to the explanatory dictionary, truth table - This tabular representation of the logical circuit (operations), which lists all possible combinations of the truth values ​​of the input signals (operands) along with the truth values ​​of the output signal (result of the operation) for each of these combinations.

Problematic question:

Why create truth tables of logical functions?

For tabular representation of a logical diagram.

Conjunction - corresponds to union and, logical multiplication.

Disjunction - corresponds to a conjunction or logical addition.

Implication – corresponds to the conjunction if...then

Equivalence - matches the word equivalent

Negation - corresponds to the conjunction not.

Truth table.

4. Consolidation of practical skills.

Exercise. Determine whether the statement is true.

A) AB→AB with A-and B-l

B) ͞АВ→А῀А with A-l B-i

B) ͞͞AB→C͞D῀U with A-i B-l S-i D-l U-i

D) (A→B)῀(AB῀͞A) with A-and B-l

D) (X῀͞U) (A→B) with X-l U-i V-l A-i

5. Summing up.

Students are encouraged to carry out mutual verification solving logical problems.

For each correct answer 1 point is awarded.

5 points – “5”

4 points – “4”

3 points – “3”

3 points – “2”

6. Reflection.

When conducting reflection, the “Sinquain” technique is used.

Sinkwine

1 I line - one noun.

2 I line - two adjectives.

3 I line - three verbs.

4 I line - one complete sentence (statement).

5 I line - one final word.

7.Assign homework.