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Show that $p\vee(p\wedge q)=p$ follows from the idempotent rule, distributive rule, and the absorption rule $p\wedge(p\vee q)=p$.

for this question i have spent 2 hours but still don't understand where to start. help here pleas!! can this also be an answer?? p∨(p∧q)=(p∨p)∧(p∨q) =p∧(p∨q) =p

KRISSH
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1 Answers1

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Using first the idempotent rule, then the distributive rule, then the "other" absorption rule, we have $$\eqalign{p\vee(p\wedge q) &=(p\wedge p)\vee(p\wedge q)\cr &=p\wedge(p\vee q)\cr &=p\ .\cr}$$

David
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