Question

Write the following statement in symbolic form and find its truth value:
∀ n ∈ N, n² + n is an even number and n² - n is an odd number.

Answer 1

Let p ≡ ∀ n ∈ N, n² + n is an even number

Let q ≡ ∀ n ∈ N, n² - n is an odd number

The symbolic form of given statement is
(p ∧ q)

Truth value of given statement is

p ≡ ∀ n ∈ N, n² + n is an even number (T)

q ≡ ∀ n ∈ N, n² - n is an odd number (F)

(∵ from n = 1, n² - n = 0, which is not an odd number)

∴ (p ∧ q) ≡ T ∧ F ≡ F

∴ the given statement is false