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Let p and q be two propositions. Consider the following two formulae in propositional logic. S1: (¬p ∧ (p ∨ q)) → q S2: q → (¬p ∧ (p ∨ q)) Which of the following is correct?

1. S1 is true and S2 is false.
2. S1 is false and S2 is true.
3. S1 is false and S2 is true.
4. Both S1 and S2 are false.

Correct answer: S1 is true and S2 is false.

Solution

S1 is true because if ¬p is true, then p is false, making the expression (p ∨ q) depend solely on q, which leads to q being true. S2 is false because it asserts that if q is true, then ¬p must also be true, which is not necessarily the case.

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