ISRO-DEC2017-6

Question

The proposition $(P\Rightarrow Q)\wedge (Q\Rightarrow P)$ is a

• A. Tautology
• B. Contradiction
• C. Contingency
• D. Absurdity

Comments

@soumya, Thanks!

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To add into below answers, the given proposition is that of biconditional statement, which itself is a contingency.

https://www.mathgoodies.com/lessons/vol9/biconditional

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What is absurdity?

Answer 1

P	Q	P->Q	Q-> P	(P->Q)^(Q->P)
T	T	T	T	T
T	F	F	T	F
F	T	T	F	F
F	F	T	T	T

The given proposition is bidirectional, which is neither tautology nor contradiction.

A proposition which is neither tautology nor contradiction is contingency.

Hence option C) is correct

Comments

what's the difference between contradiction and absurdity ?

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Contradiction and Absurdity can be used as synonyms.

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If we get all false than it is contradiction or absurdity?

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What is absurdity?

Answer 2

option c

Answer 3

From the truth table of $A\rightarrow B$, we know that $True\rightarrow False=False$, and rest all are $True$.
Take $P=True$, and $Q=False$.
Then $(True\rightarrow False)\wedge(False \rightarrow True)=False\wedge True=False.$ This proves it is not a tautology.

Take $P=Q=True.$
Then$(True\rightarrow True)\wedge(True\rightarrow True)=True\wedge True=True.$ This proves it is not a contradiction either, and since it is taking up values depending on the variables, it is a contingency.

Answer 4

As we take
P Q
TT - >T
TF - >F
FT - >F
FF - >T
(C) Not tautology ,not contradiction it is contingency.