The negation of the Boolean expression (([] q) [] p) [] (([] p) [] q) is logically equival…

Question

The negation of the Boolean expression (($$\sim$$ q) $$\wedge$$ p) $$\Rightarrow$$ (($$\sim$$ p) $$\vee$$ q) is logically equivalent to :

Accepted Answer

Let $$S:(( \sim q) \wedge p) \Rightarrow (( \sim p) \vee q)$$

$$ \Rightarrow S:\, \sim (( \sim q) \wedge p) \vee (( \sim p) \vee q)$$

$$ \Rightarrow S:(q \vee ( \sim p)) \vee (( \sim p) \vee q)$$

$$ \Rightarrow S:( \sim p) \vee q$$

$$ \Rightarrow S:p \Rightarrow q$$

So, negation of S will be $$ \sim (p \Rightarrow q)$$

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