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Q.Using the truth table, verify ∼(∼p→∼q)≡∼p∧q\sim(\sim p \rightarrow \sim q) \equiv \sim p \wedge q.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2020Subjective· 4mImportance★★★★★
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Constructing the truth table, both ∼(∼p→∼q)\sim(\sim p \rightarrow \sim q) and ∼p∧q\sim p \wedge q give the column F,F,T,FF, F, T, F, proving the equivalence.

Construct the truth table:

ppqq∼p\sim p∼q\sim q∼p→∼q\sim p \rightarrow \sim q∼(∼p→∼q)\sim(\sim p \rightarrow \sim q)∼p∧q\sim p \wedge q
TTFFTFF
TFFTTFF
FTTFFTT
FFTTTFF
…

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