Question

The negation of "∀, n ∈ N, n + 7 > 6" is ______.

Options

• ∃ n ∈ N, such that n + 7 ≤ 6

• ∃ n ∈ N, such that n + 7 ≥ 6

• ∀, n ∈ N, n + 7 ≤ 6

• ∃ n ∈ N, such that n + 7 < 6

Answer 1

The negation of "∀, n ∈ N, n + 7 > 6" is ∃ n ∈ N, such that n + 7 ≤ 6.

Explanation:

The negation of the quantifier Forevery is there exists.

Given statements ∀ "n ∈ N" such that n+ 7 > 6

∴ The negation of the given statement is

∃ n ∈ N, such that n + 7 ≤ 6.