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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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(A) (p ∧ q) → (p ∨ q)
(B) ∼ (p ∨ q) → (p ∧ q)
(C) (∼ p ∨ ∼ q) → (∼ p ∧ ∼ q)
(D) (∼ p ∧ ∼ q) → (∼ p ∨ ∼ q)
