# 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

Proof the above premises and hypothesis using Indirect proof:
Premise $1$: $P\to \mathrm{¬}R$
Premise $2$: $Q\to S$
Premise $3$: $\left(R\vee S\right)\to T$
Premise $4$: $\mathrm{¬}T$
Hypothesis: $P\vee Q$
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doraemonjrlf
HINT
An indirect proof is the same as a proof by contradiction. So: you need to assume $\mathrm{¬}\left(P\vee Q\right)$, and show that that leads to a contradiction.
which shouldn't be hard: $\mathrm{¬}\left(P\vee Q\right)$ means $\mathrm{¬}P$, so with Premise $1$ you get $R$, so $R\vee S$, and so with Premise $3$ you get $T$, which contradicts Premise $4$ $\mathrm{¬}T$. The formal details will depend on the exact nature of your proof system.