By truth table, simply take all possible combinations of p and q and find the corresponding truth values of the given questions.
However a better method to solve such questions is the BY CASE method.
For (a), Take 2 cases i.e P = True and P = False.
When P = True,
LHS = T v (T ^ q) = T v anything = T
RHS = p = T
Hence its satisfying for this case, let’s check for the other case.
When P = False,
LHS = F V (F ^ q) = F v F = F
RHS = F
Hence its satisfying for this case too.
Similarly, you can check for option (b).