# Mathematics Questions and Answers – Mathematical Reasoning – Implications

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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

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

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

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

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

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

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

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

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

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

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

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

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.

To practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

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