01204211/activity2 logic and proofs

This is part of 01204211-58.

: This is under construction..

Inference rules

This part should be attempted after the instructor has discussed exhaustive proof technique and inference rules.

4. Use a truth table to prove Hypothetical syllogism. That is show that the conclusion $P\Rightarrow R$ logically follows from hypotheses $P\Rightarrow Q$ and $Q\Rightarrow R$.

5. Use inference rules and standard logical equivalences to show that hypotheses

• $P\Rightarrow R$
• $Q\Rightarrow R$

leads to the conclusion $(P\vee Q)\Rightarrow R$.

6. Use inference rules and standard logical equivalences to show that hypotheses

• $P\Rightarrow Q$
• $P\Rightarrow \neg Q$

leads to the conclusion $\neg P$.

7. Using inference rules to argue that if we assume

• $\neg P\Rightarrow Q$,
• $(P\vee R)\Rightarrow \neg S$,
• $W\Rightarrow S$, and
• $\neg Q$

then we can conclude that $W$ is false.

8.

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