Official solution
The truth table
p
q
\[ \sim \] p
\[ \sim \] q
p \[ \wedge \] q
p \[ \wedge \] \[ \sim \] q
p \[ \wedge \] q \[ \Leftrightarrow \] p \[ \wedge \] \[ \sim \] q
T
T
F
F
T
F
F
T
F
F
T
F
T
F
F
T
T
F
F
F
T
F
F
T
T
F
F
T
Clearly p \[\wedge\] q \[\Leftrightarrow\] p \[\wedge\] \[\sim\] q \[\equiv\] \[\sim\] p
\[\therefore\] r = q