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  4. Simplify (p ∨ q) ∧ (p ∨ ∼ q )

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Q. Simplify $ \left(p \vee q\right) \wedge \left(p \vee \sim q \right) $

MHT CETMHT CET 2009

Solution:

$(p \vee q) \wedge(p \vee\sim q)$
$=p \vee(q \wedge \sim q)\,\,\,\,$ (distributive law)
$=p \vee 0\,\,\,\,$(complement law)
$=p\,\,\,\,\,(0$ is indentity for $v )$