Answer
$\underline{\ p\ |\ q\ |\ \lnot p\ |\ \lnot q\ |\ if\ (p \lor q)\lor(\lnot p \land q)\ then\ q}$
$\ T |\ T |\ \ F\ \ |\ \ F\ \ |\ T$
$\ T |\ F |\ \ F\ \ |\ \ T\ \ |\ F$
$\ F |\ T |\ \ T\ \ |\ \ F\ \ |\ T$
$\ F |\ F |\ \ T\ \ |\ \ T\ \ |\ T$
Work Step by Step
$(p \lor q) \lor (\lnot p \land q) \rightarrow q$
Set up a table with all the possible combinations of T/F values for p and q. Evaluate the if/then statement. When the if element is T and then element is F, the statement is F. In all other cases the statement is T.
$\underline{\ p\ |\ q\ |\ \lnot p\ |\ \lnot q\ |\ if\ (p \lor q)\lor(\lnot p \land q)\ then\ q}$
$\ T |\ T |\ \ F\ \ |\ \ F\ \ |\ if\ T\ then\ T\longrightarrow T$
$\ T |\ F |\ \ F\ \ |\ \ T\ \ |\ if\ T\ then\ F\longrightarrow F$
$\ F |\ T |\ \ T\ \ |\ \ F\ \ |\ if\ T\ then\ T\longrightarrow T$
$\ F |\ F |\ \ T\ \ |\ \ T\ \ |\ if\ F\ then\ F\longrightarrow T$
