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Logically equivalent by developing a series of logical equivalence.

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Logically equivalent by developing a series of logical equivalence.

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written 7 months ago by | modified 8 weeks ago by |

Prove $\sim$ (PV( $\sim$ p^q)) and $\sim$ P ^ $\sim q$ are logically equivalent by developing a series of logical equivalence.

**solution :**

Lets consider,

$\sim$ (pv ($\sim$ p ^ q))

= $\sim$ p ^ $\sim$ (\sim p ^ q) $\rightarrow$ Demorgan's Law

= $\sim$ p ^ p v $\sim$ q $\rightarrow$ Law of negation.

= ($\sim$ p ^ p) v ($\sim$ p ^ $\sim$ q) $\rightarrow$ Distributive law

= F V ($\sim$ p ^ $\sim$ q) $\rightarrow$ $\sim$ p ^ p = F

= $\sim$ p ^ $\sim$ q $\rightarrow$ Identity law.

**Note : Verification by truth table.**

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