Among the statements: (S1): () () is a tautology. (S2): () () is a contradiction. Choose the correct answer from the options given below:

Among the statements: (S1): () () is a tautology. (S2): () () is… — Solution | JEE Mathematics

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Among the statements:

(S1): $(\phi \implies \psi) \vee (\neg \phi \implies \psi)$ is a tautology.

(S2): $(\psi \implies \phi) \implies (\neg \phi \implies \psi)$ is a contradiction.

Choose the correct answer from the options given below:

Correct answer:C

Standard Method

Given:

Find: Which of the two statements is true.

From the truth table shown in the solution image:

For (S1), the final column of $(\phi \implies \psi) \vee (\neg \phi \implies \psi)$ contains both T and F entries. Therefore, it is not a tautology.

For (S2), the final column of $(\psi \implies \phi) \implies (\neg \phi \implies \psi)$ is F for all cases. Therefore, it is a contradiction.

Hence, (S1) is false and (S2) is true.

Therefore, the correct option is A.

Assuming that an implication is always true without checking all truth-value cases is incorrect. A tautology must be true in every row of the truth table. Construct the full truth table before concluding.
Confusing 'not a tautology' with 'contradiction' is wrong. A contradiction is false in every case, whereas a non-tautology may be true in some rows and false in others. Check the entire final column carefully.
Mixing up the direction of implication, such as treating $\psi \implies \phi$ the same as $\phi \implies \psi$ , gives incorrect truth values. Evaluate each implication exactly as written.

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