Give an example of a statement P(n) which it true for all n ≥ 4 but P(1), P(2) and P(3) are not true. Justify your answer.

Given; P(n) which it true for all n ≥ 4 but P(1), P(2) and P(3) are not true

Let P(n) be 2ⁿ < n!

This statement is true for all n ≥ 4 but P(1), P(2) and P(3) are not true.

i.e P(0) ⇒ 2⁰ < 0! i.e 1 < 1 Which is not true

P(1) ⇒ 2¹ < 1! i.e 2 < 1 Which is not true

P(2) ⇒ 2² < 2! i.e 4 < 2 Which is not true

P(3) ⇒ 2³ < 3! i.e 8 < 6 Which is not true

P(4) ⇒ 2⁴ < 4! i.e 16 < 24 Which is true

P(5) ⇒ 2⁵ < 5! i.e 32 < 60 Which is true

And so on.