"Mathematical Reasoning - Implications"

1. If p then q means if p is ________ then q must be ______________

a) true, true

b) true, false

c) false, false

d) false, true

2. If p then q means ___________________

a) If q then p

b) p => q

c) q => p

d) q only if p

3. If p then q means ______ is sufficient condition for ____________

a) p, p

b) q, q

c) p, q

d) q, p

4. If p then q means ___________ only if ___________

a) p, q

b) q, p

c) p, p

d) q, q

5. If p then q means ______ is necessary condition for ____________

a) p, p

b) q, q

c) p, q

6. If p then q means _________ implies __________

a) q => p

b) ~q => ~p

c) ~p => ~q

d) p => ~q

7. What is contrapositive for statement if p then q?

a) if not q then not p

b) if q then p

c) if not p then q

d) if not p then not q

8. Which of the following is contrapositive of "If x is divisible by 4 then x must be divisible by 2"?

a) If x is divisible by 2 then x must be divisible by 4

b) If x is not divisible by 2 then x must be divisible by 4

c) If x is not divisible by 2 then x is not divisible by 4

d) If x is divisible by 4 then x is not divisible by 2

9. What is converse for statement if p then q?

a) if not q then not p

b) if q then p

c) if not p then q

d) if not p then not q

10. Which of the following is converse of "If x is divisible by 4 then x must be divisible by 2"?

a) If x is divisible by 2 then x must be divisible by 4

b) If x is not divisible by 2 then x must be divisible by 4

c) If x is not divisible by 2 then x is not divisible by 4

d) If x is divisible by 4 then x is not divisible by 2