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Among the two statements (S1) : (p ⇒ q) ∧ (p ∧ ~(q)) is a contradiction and (S2) : (p ∧ q) ∨ ((~p ∧ q) ∨ (p ∧ (~q)) ∨ ((~p ∧ ~q)) is a tautology (1) only (S2) is true (2) only (S1) is true (3) both are false (4) both are true

1. only (S2) is true
2. only (S1) is true
3. both are false
4. both are true

Correct answer: both are true

Solution

Both statements are true because (S1) represents a logical contradiction, as it cannot be true under any circumstances, while (S2) encompasses all possible truth values of p and q, making it a tautology.

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