Solution to Show following equivalence without considering the truth table. (๐‘ฬ… โˆง( ๐‘žฬ…โˆง๐‘Ÿ)) โˆจ(๐‘ž โˆง๐‘Ÿ) โˆจ(๐‘ โˆง๐‘Ÿ)โ†”๐‘Ÿ - Sikademy
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Archangel Macsika

Show following equivalence without considering the truth table. (๐‘ฬ… โˆง( ๐‘žฬ…โˆง๐‘Ÿ)) โˆจ(๐‘ž โˆง๐‘Ÿ) โˆจ(๐‘ โˆง๐‘Ÿ)โ†”๐‘Ÿ

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(\lnot p \land(\neg q \land r))\lor(q\land r) \lor(p\land r)\leftrightarrow(r \land(\neg q \land \neg p))\lor(r\land (q\lor p)) \leftrightarrow

\leftrightarrow r\land ((\lnot p \land \lnot q) \lor (q \lor p)) \leftrightarrow r\land (\lnot(p\lor q) \lor (p\lor q)) \leftrightarrow r\land 1 \leftrightarrow r


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Question ID: mtid-5-stid-8-sqid-1398-qpid-1136