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1.Show that $\neg((\neg p\land q)\lor(\neg p\land \neg q))\lor(p\land q)\equiv p.$

$\neg((\neg p\land q)\lor(\neg p\land \neg q))\lor(p\land q)\equiv \neg(\neg p\land ( q\lor \neg q))\lor (p\land q)\equiv \neg(\neg p\land q)\lor (p\land q)\equiv (p\lor \neg q)\lor (p\land q).$

I stuck here. I am very beginner in logics and propositional calculus. Any help will be appreciated.

Unknown
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    Since $q\lor \neg q$ must be true, $\neg p\land (q\lor\neg q)\iff \neg p$ and therefore the proposition is equivalent to $p\lor (p\land q)$, which is thus equivalent to $p$. – justadzr Dec 22 '20 at 19:17
  • @Yourong'DZR'Zang Thanks Sir! – Unknown Dec 22 '20 at 19:38

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