Q.Determine the truth values of p and q in the following case: $(p \land q)$ is F and $(p \land q) \to q$ is T

The first condition directly states p∧q=F. Now examine the second condition: (p∧q)→q. Since we are already told p∧q=F, the antecedent of this conditional is F, and a conditional with a false antecedent is ALWAYS true, regardless of the truth value of q. So (p∧q)→q=T is automatically satisfied whenever p∧q=F — it adds no new information.

So we only need p∧q=F, which holds for three of the four combinations: (p=T,q=F), (p=F,q=T), and (p=F,q=F). Only (p=T,q=T) is excluded (since that makes p∧q=T). …

Assuming every 'determine p and q' problem has a single unique answer — here the second condition is vacuous given the first, so multiple soluti …