Question

Write the negation of the statement.

‘∃ n ∈ N such that n + 8 > 11’

Answer 1

To negate the existential quantifier (∃), we use the logical rule:

∼ (∃ n ∈ N, P (n)) ≡ ∀ n ∈ N, ∼ P(n)

Here, P(n) is the statement n + 8 > 11, so its negation is:

n + 8 ≤ 11

∀ n ∈ N, n + 8 ≤ 11