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

  1. Tautology
  2. Contradiction
  3. Contingency
  4. Absurdity
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6 Answers

Best answer
10 votes
10 votes
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

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1 votes
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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:

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