Assume that all of the following are true(P ∨ Q) ⇒ RQ ∨ RR ⇒ PShow by contradiction that P is true.3

To prove P by contradiction, we first assume that P is not true.

1. Assume ~P (P is not true)
2. From the first statement, (P ∨ Q) ⇒ R, since we assumed ~P, we have Q ⇒ R (because if P is not true in a disjunction, the other must be true for the disjunction to hold)
3. From the second statement, Q ∨ R ⇒ P, but we assumed ~P, so we must have ~Q and ~R (because if P is not true in a disjunction, the other must be false for the disjunction to hold)
4. But from step 2, we have Q ⇒ R, which contradicts with ~Q and ~R from step 3.

Therefore, our assumption that ~P is false, which means P must be true.