(i) Let us assume that p is not true.
∴ Sum of an irrational and a rational number is not irrational.
⇒ There exists an irrational number a and a rational number b such that a + b is not irrational.
⇒ a + b = c (say) is a rational number. ⇒ a = c – b ⇒ a is rational
But a is irrational, which is a contradiction.
So, our supposition is wrong. Thus, p is true.
(ii) Suppose n > 3 but n2 ≯ 9 ⇒ n2 ≤ 9
⇒ n2 – 9 ≤ 0 ⇒ (n – 3)(n + 3) ≤ 0 ⇒ –3 ≤ n ≤ 3
which is a contradiction as n > 3. So our supposition is wrong.
If n is a real number with n > 3, then n2 > 9.