Write the negations of the following statements:
(a) All students of this college live in the hostel.
(b) $6$ is an even number or $36$ is a perfect square.

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Solution

$(a) p :$ All students of this college live in the hostel.

Negation: $\sim p :$ Some students of this college do not live in the hostel.

$(b) p : 6$ is an even number or $q : 36$ is a perfect square.

Symbolic form: $p \lor q$

$∴ \sim (p \lor q) \equiv\sim p \land \sim q$

Negation: $6$ is not an even number and $36$ is not a perfect square.

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