Variant 1

18. Which of the following statement is a proposition?
A) Get me a glass of milkshake
B) God bless you!
C) What is the time now?
D) The only odd prime number is 2

19. The compound propositions p and q are called logically equivalent if ________ is a tautology.
A) p ↔ qB) p → qC) (p ∨ q)D) p ∨ q

20. The set O of odd positive integers less than 10 can be expressed by _____________
A) {1, 2, 3}
B) {1, 3, 5, 7, 9}
C) {1, 2, 5, 9}
D) {1, 5, 7, 9, 11}

21. What is the cardinality of the set of odd positive integers less than 10?
A) 10B) 5C) 3D) 20

22. If p is any statement, then which of the following is a tautology?
A) p∧ F
B) p∨ F
C) p∨ p
D) p∧ T

23. (p∨ q) ∧ (p∧ q) is a ___________
A) TautologyB) ContradictionC) ContingencyD) None of the mentioned

24. Let p: This is a great website, q: You should not come back here.
Then ‘This is a great website and you should come back here. ’ is best represented by:
A) p ∨ q
B) p∧ q
C) p ∨ q
D) p∧ q

25. Which of the following statements is the negation of the statements “4 is odd or -9 is positive”?
A) 4 is even or -9 is not negative
B) 4 is odd or -9 is not negative
C) 4 is even and -9 is negative
D) 4 is odd and -9 is not negative

(26-30) 2 points.

26) Let p and q be the propositions “It is below freezing” and “It is snowing” respectively. Express the proposition ( pÚ q) Ù ( p ® q) as an English sentence.

27)The propositions p and q are logically equivalent if

28)When the statement " y$xØ P(x, y) is false?

29) Let U={0, 1, 2, 3, 4, 5, 6, 7, 8, 9}be the universal set, and let A={5, 1, 3, 4, 7, 8}, B={1, 2, 4, 6, 7, 5, 9}. Find .

30)

31)Prove that if x³ is irrational, then x is irrational.

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