Answer
Truth tables:
Work Step by Step
For 13a: First fill in the 4 possible combinations of truth values for p and q. Then fill in the column for ~p. Evaluate the if/then statement (p $\rightarrow$ q). When the if element is T and then element is F, the statement is F. In all other cases the statement is T. Then evaluate ~p $\lor$ q according to the definition of OR (a $\lor$ b is true when either a is true, or b is true, or both a and b are true; it is false only when both a and b are false). Notice that (p $\rightarrow$ q) and (~p $\lor$ q) always share the same truth values, so they are logically equivalent.
For 13b. Evaluate ~(p $\rightarrow$ q) by taking the negation of the truth values of (p $\rightarrow$ q) from the truth table for 13a. Fill in the values for ~q, then evaluate p $\land$ ~q according to the definition of AND (a $\land$ b is true when, and only when both a and b are true).
