Question

Show that (~𝒑∨𝒒)∧(𝒑∧~𝒒) is a contradiction

Answer 1

$\left( {\~p \vee q} \right) \wedge \left( {p \wedge \~q} \right) = \left( {\~p \wedge p \wedge \~q} \right) \vee \left( {q \wedge p \wedge \~q} \right) = \left( {\left( {\~p \wedge p} \right) \wedge \~q} \right) \vee \left( {\left( {q \wedge \~q} \right) \wedge p} \right) = \left( {0 \wedge \~q} \right) \vee \left( {0 \wedge p} \right) = 0 \vee 0 = 0$

Q.E.D.