Proof the above premises and hypothesis using Indirect proof Premise 1: P→¬R Premise 2: Q→S Premise 3: (R∨S)→T Premise 4: ¬T Hypothesis: P∨Q

gemauert79 2022-09-24 Answered
Proof the above premises and hypothesis using Indirect proof:
Premise 1: P ¬ R
Premise 2: Q S
Premise 3: ( R S ) T
Premise 4: ¬ T
Hypothesis: P Q
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Answers (1)

doraemonjrlf
Answered 2022-09-25 Author has 8 answers
HINT
An indirect proof is the same as a proof by contradiction. So: you need to assume ¬ ( P Q ), and show that that leads to a contradiction.
which shouldn't be hard: ¬ ( P Q ) means ¬ P, so with Premise 1 you get R, so R S, and so with Premise 3 you get T, which contradicts Premise 4 ¬ T. The formal details will depend on the exact nature of your proof system.
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