This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “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

View Answer

Explanation: If p then q means if p is true then q must be true. It says nothing when p is false. If p is false then q might be true or false.

2. If p then q means ___________________

a) If q then p

b) p => q

c) q => p

d) q only if p

View Answer

Explanation: If p then q means p implies q i.e. p => q. This does not mean q => p.

Q only if p means q=>p.

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

a) p, p

b) q, q

c) p, q

d) q, p

View Answer

Explanation: If p then q means p is sufficient condition for q or p=>q. It is not same as q is sufficient condition for p.

4. If p then q means ___________ only if ___________

a) p, q

b) q, p

c) p, p

d) q, q

View Answer

Explanation: If p then q means p only if q or p=>q which is not same as q only if p or q=>p.

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

a) p, p

b) q, q

c) p, q

d) q, p

View Answer

Explanation: If p then q means q is necessary condition for p or p => q. It is not same as p is necessary condition for q.

6. If p then q means _________ implies __________

a) q => p

b) ~q => ~p

c) ~p => ~q

d) p => ~q

View Answer

Explanation: If p then q means p => q or negation of q implies negation of p i.e. ~q => ~p.

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

View Answer

Explanation: Contrapositive statement for given statement “if p then q” is “if not q then not p” i.e. ~q => ~p.

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

View Answer

Explanation: Contrapositive statement for given statement “if p then q” is “if not q then not p” i.e. ~q => ~p.

So, contrapositive for “If x is divisible by 4 then x must be divisible by 2” is “If x is not divisible by 2 then x is not divisible by 4”.

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

View Answer

Explanation: Converse statement for given statement “if p then q” is “if q then p” i.e. q => p or q implies p.

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

View Answer

Explanation: Converse statement for given statement “if p then q” is “if q then p” i.e. q => p.

So, converse for “If x is divisible by 4 then x must be divisible by 2” is “If x is divisible by 2 then x is must be divisible by 4”.

11. Is meaning of p if and only if q and q if and only if p is same?

a) True

b) False

View Answer

Explanation: If we write “q if and only if p” then it means q <=> p i.e. p=> q and q=> p.

And if we write “p if and only if q” then it means p <=> q i.e. q=> p and p=> q.

So, both are exactly same.

12. Is meaning of p only if q and q only if p is same?

a) True

b) False

View Answer

Explanation: If we write “q only if p” then it means q => p.

And if we write “p only if q” then it means p => q.

So, both are different.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 11**.

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