Question

Write the negations of the following statements :

1) All students of this college live in the hostel

2) 6 is an even number or 36 is a perfect square.

Answer 1

1) p: All students of this college live in the hostel.

Negation :

~ p: Some students of this college do not live in the hostel.

2) 

p: 6 is an even number.
q: 36 is a perfect square.

Symbolic form : p v q

∴ ~(p v q) ≡ ~p ∧ ~q

Negation :

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