Using indirect method show that R->¬Q,R ∨ S,S->Q,P->¬Q=¬P.
With detailed steps and also easy to understand.
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Using indirect method show that R->¬Q,R ∨ S,S->Q,P->¬Q=¬P.
With detailed steps and also easy to understand.
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Step-by-step explanation:
To show \( R \rightarrow \neg Q, R \lor S, S \rightarrow Q, P \rightarrow \neg Q \) implies \( \neg P \) using an indirect method:
1. Assume \( P \).
2. Since \( P \rightarrow \neg Q \), it follows that \( \neg Q \).
3. Considering \( R \lor S \) and \( \neg Q \), if \( R \) is true, then we have \( R \rightarrow \neg Q \) satisfied.
4. If \( S \) is true, and \( S \rightarrow Q \), then \( Q \) is true, contradicting \( \neg Q \).
5. Therefore, the assumption \( P \) leads to a contradiction.
6. Consequently, the negation \( \neg P \) must be true.
So, \( R \rightarrow \neg Q, R \lor S, S \rightarrow Q, P \rightarrow \neg Q \) implies \( \neg P \) indirectly.