You can also use truth table to verify that your answer is correct.
For proposition which have the form of implication there is a shorter way:
Clearly if false only in one case: p=1, q=0.
Let us try to the same thing with the first expression
This implication is false only if and q=0. For a conjunction to be true, you need that both of the operands are true. This means that p=1, and is also true for p=1,q=0.