ict

No.

Stage

Time (min)

1.

Organizing time.

2

2.

Target setting

3

3.

Learning new material.

17

4.

Consolidation of the acquired knowledge

eleven

five.

Summarizing

five

6.

Homework

2

Lesson stage

Teacher actions

Student actions

1.

Greet students, create a welcoming classroom environment, check attendees with clickers

Greeting the teacher, checking the readiness of the workplace, setting up for educational activities

2.

How does a person think? What is a statement in our speech and what is not? What are the similarities and differences in arithmetic multiplication and logical multiplication?

We will try to answer these and some other questions today in the lesson. We will also get acquainted with the basic logical expressions and operations, we will learn some of the components of our thinking.

So, the topic of our lesson is Elements of propositional logic.

Write down the topic of the lesson

3.

Psychologists have long established that a person's mental activity is always carried out through a language. The use of language gives thought activity the form of reasoning. What is reasoning?­

Reasoning - This is a sequence of questions asked to oneself or the interlocutor, and the answers to them.­

Questions can be of different types. You might ask, "How many prime numbers are there?" The answer is the statement: "There are infinitely many prime numbers." You might ask, "How do you find the thousandth prime?" The answer is an algorithm that calculates the required prime. Recall that the information contained in the answer to the first question, we refer to the declarative type, and the information contained in the answer to the second question - to the procedural one.­­­

Information presented declaratively can be assessed from only one position - whether it is true or false.­­

A declarative sentence, in relation to which it makes sense to talk about its truth or falsity, is called a statement. This definition of the statement was given by Aristotle. Consider the following suggestions.­

1. The number √2 is irrational.

2. The number √2 is rational.

3. Any natural number x is rational.

4. Any number x is rational.

5. There is a number x that is irrational.

6. The number x is rational.

7. If the number x is irrational, then the number x + 1 is also irrational.

8. A number is called rational if it is equal to the ratio of an integer to a natural number.­

9. Is it true that the number √2 is irrational?

10.          Prove that the number √2 is irrational.

What sentences are utterances? What do you think?

Discussion of correct answers.

Leaving other sciences the right to answer the question about the truth of a particular statement, logic is interested in how new true statements can be obtained from a set of true statements. This means that logic studies such operations on statements, as a result of which the statement is again obtained. Mathematical logic offers a formalized language for describing these operations, which allows us to build a formal model of human reasoning.­­

You are probably familiar with some logical operations from the basic computer science course. This is primarily the operation of conjunction (in another way, the operation and), disjunction (in another way, the operation or) and the operation of negation (in another way, the operation is not). But there are other operations, they are listed in the table­­

The values ​​of logical operations are set, as you know, using truth tables. They record the result of applying the operation for all possible combinations of argument values. For all operations at the same time, these tables are collected in a table; in it, the values ​​of the arguments and the result of applying the operation are indicated by the letters "I" (True) and "L" (False).­­­­

As can be seen from the table, the truth of a statement obtained with the use of disjunction takes place when either one statement is true, or the other, or both at the same time. For example, the truth of the statement "It is raining or the wind is blowing" means that one of three situations occurs on the street: it is raining and there is no wind; there is no rain, but the wind blows; it rains and the wind blows at the same time. Therefore, writing this phrase by means of mathematical logic, it is natural to represent it in the form XVY, where X is the statement "It is raining", and Y is the statement "The wind is blowing."­­

Usually, with the help of logical operations, they try to reduce any statement to such statements, in which it is no longer possible to single out other statements. Such statements, no part of which is a statement, are called simple.­

Listen

Write a definition

Write a definition

Using an interactive polling system, statements are selected, and then true statements.

Write in a notebook

Write in a notebook

4.

Exercise 1.

Create a truth table for statements:

¬Y → ¬X

X → (Y → X)

Exercise 2.

Find the values ​​of the boolean expressions:

F = (0v0) v (lvl)

F = (0 & 0) & (1 & 1) (answer: 0)

Testing using an interactive survey system.

1. Which of the sentences are statements.

A.    How long is this tape?

B.    Listen to the message.

C.    Name the input device.

D.    Who is absent?

E.     Paris is the capital of England. (FALSE)

F.     The number 11 is prime. (TRUE)

G.    4 + 5 = 10. (FALSE)

H.    You can't get a fish out of the pond without difficulty.

I.       Some bears live in the north. (TRUE)

J.       All bears are brown. (FALSE)

2. Which of the following statements are simple?

A.    1234 is even and divisible by 3;

B.     the number 1234 is odd and divisible by 3;

C.     1234 is even or not divisible by 3;

D.    1234 is odd or not divisible by 3.

3. Find the values ​​of the logical expressions:

F = (lvl) v (lv0)

(answer: 1)

4. Find the values ​​of the logical expressions:

F = ┐1 & (1 v1) v (┐0 & 1) (answer: 1)

5. What logical expression corresponds to the statement: "Point X belongs to the interval (A; B)".

A.    (X <A) or (X> B)

B.    (X> A) and (X <B)

C.    Not (X <A) or (X <B)

D.    (X> A) or (X> B)

Do the task in the notebook

Answering questions individually using "clickers"

five.

Frontal conversation with students on the topic of the lesson.

Grading.

6.

Homework - learn basic definitions, know the notation.

Create a truth table for statements:

X v Y → (X & Y);

¬ (X & Z) → (Y v Z → X)

Writing homework in a diary