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Ace Test Series: Mathematical Logic - Propositional Logic

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Okay I don't know how far my approach to this question is correct. Please correct me if I'm wrong.

S1:

Since (p->q) is false, p = 1, q = 0(from implication truth table)

Put the values of p and q in the next part and it is false. Hence S1 is false.

S2:

For S2 try all the remaining 3 possibilities of p and q in the next part and all comes true. Hence S2 is false too.

Answer: Option D

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