MTH401

1. What is the negation of the statement "All cats can fly"?

a) No cats can fly b) Some cats can't fly c) All cats can't fly d) Some cats can fly

2. Which of the following is a propositional variable?

a) 2+2=4 b) p implies q c) (x+1)(x-1)=x^2-1 d) There are no unicorns

3. Which of the following is a tautology?

a) p xor q b) p implies q c) p and (not p) d) p or (not p)

4. What is the contrapositive of the statement "If it rains, then I stay inside"?

a) If I don't stay inside, then it doesn't rain. b) If I stay inside, then it doesn't rain. c) If it doesn't rain, then I don't stay inside. d) If it doesn't rain, then I stay inside.

5. Which of the following is equivalent to "not (p or q)"?

a) not p and not q b) not p or not q c) p and q d) p or q

6. Which of the following is a valid propositional equivalence?

a) p and q = p or q b) p implies q = q implies p c) p xor q = not p d) p and (not p) = p or (not p)

7. Which of the following is a universal quantifier?

a) There exist b) For all c) or d) implies

8. What is the converse of the statement "If it is raining, then the streets are wet"?

a) If the streets are wet, then it is raining. b) If it is not raining, then the streets are not wet. c) If the streets are not wet, then it is not raining. d) If it is wet outside, then it is raining.

9. Which of the following is equivalent to "not (p implies q)"?

a) p and not q b) not p and not q c) p and q d) not p or q

10. Which of the following is a valid propositional equivalence?

a) p and q = q or p b) p implies q = not p or q c) p xor q = not p and not q d) p or (not q) = not (p and q)

Math MCQs

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