#### 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.

#### Solution

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.

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#### APPEARS IN

Solution Write the Negations of the Following Statements : All Students of this College Live in the Hostel and 6 is an Even Number Or 36 is a Perfect Square. Concept: Mathematical Logic - Sentences and Statement in Logic.