Ict

Tasks for the "Logic" module

1.      For which name is the saying true:

¬ (First letter of a vowel name -> Fourth letter of a consonant)

1) ELENA 2) VADIM 3) ANTON 4) FEDOR

2.      For which name is the saying true:

First letter of name consonant ^ (¬ Second letter of name consonant -> Fourth letter of name vowel)

1) IVAN 2) PETER 3) PAUL 4) ELENA

3.      For what number X is the statement (X> 4) v ((X> 1) -> (X> 4)) true?

1) 1 2) 2 3) 3 4) 4

4. Indicate which logical expression is equivalent to the expression ¬ (¬A ^ B)

1) A v¬B 2) ¬A vB 3) B ^ ¬A 4) A ^ ¬ B

5. Indicate which boolean expression is equivalent to expression

 (A-> B) -> (¬B-> ¬A)

1) A v¬ B 2) ¬Av¬B 3) 1 4) A ^ ¬ B

6. Simplify the expression ¬ (¬X ^ ¬Y)

7. Simplify the expression (¬X vY) ^ X

8. Symbol F denotes one of the following logical expressions from three arguments X, Y, Z

A fragment of the truth table of expression F

What is F? 1) ¬X ^ ¬Y ^ Z 2) ¬Xv¬YvZ 3) X vY v¬Z 4) X vY vZ

9. Symbol F denotes one of the following logical expressions from three arguments X, Y, Z

A fragment of the truth table of expression F

What is F? 1) ¬X v¬Y v ¬Z 2) X ^ ¬Y ^ ¬Z 3) X ^ Y ^ Z 4) X vY vZ

10. How many different solutions does the equation ((¬N ^ ¬M) vL) -> ((K ^ ¬L) vM) = 1

11. Specify the values ​​of the variables K, L, M, N, at which the logical expression

(KvM) -> (¬LvMvN) is false.

12. X, Y, Z are integers for which the statement is true

((Z <X) v (Z <Y)) ^ ¬ ((Z + 1) <X) ^ ¬ ((Z + 1) <Y)

What is Z if X = 20, Y = 10

13. Mom, who came running to the sound of a broken vase, found all three of her sons in completely innocent positions: Sasha, Vanya and Kolya pretended that what had happened did not apply to them. However, the soccer ball among the fragments clearly indicated otherwise.

- Who did this? - asked mom

- Kolya did not hit the ball, - said Sasha. - Vanya did it

Vanya replied: - Kolya broke, Sasha did not play football at home.

- So I knew that you would blame each other, - my mother was angry. - Well, what do you say? - she asked Kolya.

- Don't be angry, mommy! I know that Vanya couldn't do it. And I haven't done my homework yet, - said Kolya.

It turned out that one of the boys lied twice, and two in each of their statements spoke the truth. Who broke the vase?

14. Some key word is pondering. A series of words is given as long as the intended word. After each word, the number of letters matching the keyword is written, separated by a colon:

FREEDOM: 2 SHEEP: 2 OBZ: 2 CRANE: 0

It is required to define a keyword.

15. How many records in the table satisfy the condition (A = 1 ^ B = 2) v (C = 3 ^ B = 2)

1) 2 2) 3 3) 4 4) 1

17. Three witnesses to the road accident reported information about the escaped intruder. Bob claims that he was in a blue Renault, John said that the intruder left in a black Toyota, and Sam showed that the car was definitely not blue and, most likely, it was a Ford. When we managed to find the car, it turned out that each of the witnesses accurately determined only one of the parameters of the car, and made a mistake in the other. What and what color was the offender's car?

18. Three schoolchildren Misha, Kolya and Sergei, who remained in the classroom during recess, were summoned to the headmaster about the broken window in the office. When the director asked who did it, the boys answered the following:

Misha: "I didn't break the window, and neither did Kolya"

Kolya: "Misha did not break the window, Sergey broke it with a soccer ball!"

Sergey: "I didn't do it, Misha broke the glass"

It became known that one of the guys told the pure truth, the second lied in one part of the statement, and his other statement was true, and the third distorted both facts. Who broke the window?