Given two propositional statements Px and Ax with x in a dom

Given two propositional statements P(x) and A(x) with x in a domain of definition. We are given the statement which we call S: P(x) rightarrow A(x) If we know this statement is false, what can we say about P (if anything)?

Solution

If A and B are 2 propositional statements, then,

A --> B is false only when A is true and B is false.

so, here, in this question,

if P(x) ---> A(x) is false, P must be true.