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
View Answer

Answer: a
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.
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2. If p then q means ___________________
a) If q then p
b) p => q
c) q => p
d) q only if p
View Answer

Answer: b
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

Answer: c
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.
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4. If p then q means ___________ only if ___________
a) p, q
b) q, p
c) p, p
d) q, q
View Answer

Answer: a
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

Answer: d
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.
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6. If p then q means _________ implies __________
a) q => p
b) ~q => ~p
c) ~p => ~q
d) p => ~q
View Answer

Answer: b
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

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

Answer: c
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

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

Answer: a
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

Answer: a
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

Answer: b
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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter