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Implication

The negation ...

Question

The negation of the statement "if $5 > 7$ then, $6 < 4$ "

(5 > 7) \land (6 \geq 4)

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(5 > 7) \lor (6 \leq 4)

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(5 \leq 7) \lor (6 \leq 4)

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(5 \leq 7) \land (6 \leq 4)

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Solution

The correct option is A $(5 > 7) \land (6 \geq 4)$
Let $p : 5 > 7; q : 6 < 4$ ;
We know that the negation of implication is given as $\sim (p \to q) = p \land \sim q$
So the negation of the statement "if $5 > 7$ then, $6 < 4$ " is $(5 > 7) \land (6 \geq 4)$

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