Prove-the-following-is-a-tautology-p-q-p-r-q-r-

Question Number 198750 by depressiveshrek last updated on 24/Oct/23

Prove the following is a tautology :

[(p ⊻ q) \land (p \Rightarrow r)] \Rightarrow (q ⊻ r)

Answered by MathematicalUser2357 last updated on 29/Dec/23

Only know until

=\sim [(p ⊻ q) \land (\sim p \lor r)] \lor (q ⊻ r)

= (p \bar{⊻} q) \lor p \land \sim r \lor (q ⊻ r)

=\sim p \land \sim q \lor p \land q \lor p \land \sim r \lor \sim p \land r

= p \lor q \lor r \land (\sim p \lor \sim r)