Question

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.

Answer 1

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

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

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

Symbolic form: $p\vee q$

$\therefore \sim (p\vee q)\equiv \sim p\wedge \sim q$

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