Answer
Truth table for p $\land$ ~r $\leftrightarrow$ q $\lor$ r:
Work Step by Step
First fill in the eight possible combinations of truth values for p, q, and r. Then fill in ~r. Then fill in the column for p $\land$ ~r according to the definition of AND (p $\land$ ~r is true when, and only when, both p and ~r are true. If either p or ~r is false, or if both are false, p $\land$ ~r is false). Then fill in q $\lor$ r according to the definition of OR (q $\lor$ r is true when either q is true, or r is true, or both q and r and true; it is false only when both q and r are false). Then fill in the column for p $\land$ ~r $\leftrightarrow$ q $\lor$ r according to the definition of biconditional (a $\leftrightarrow$ b is true if both a and b have the same truth values and is false if a and b have opposite truth values).
