Answer
Truth table for (p $\rightarrow$ r) $\leftrightarrow$ (q $\rightarrow$ r):
Work Step by Step
First fill in the eight possible combinations of truth values for p, q, and r. Evaluate the if/then statements on either side of the biconditional, first (p $\rightarrow$ r), second (q $\rightarrow$ r). When the if element is T and then element is F, the statement is F. In all other cases the statement is T.
Lastly evaluate (p $\rightarrow$ r) $\leftrightarrow$ (q $\rightarrow$ r) according to the definition of bioconditional (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).
