Question:
Give an example of a statement P(n) which is true for all n ≥ 4 but P(1), P(2) and P(3) are not true. Justify your answer.
Solution:
According to the question,
P(n) which is true for all n ≥ 4 but P(1), P(2) and P(3) are not true
Let P(n) be 2n < n!
So, the examples of the given statements are,
P(0) ⇒ 20 < 0!
i.e 1 < 1 ⇒ not true
P(1) ⇒ 21 < 1!
i.e 2 < 1 ⇒ not true
P(2) ⇒ 22 < 2!
i.e 4 < 2 ⇒ not true
P(3) ⇒ 23 < 3!
i.e 8 < 6 ⇒ not true
P(4) ⇒ 24 < 4!
i.e 16 < 24 ⇒ true
P(5) ⇒ 25 < 5!
i.e 32 < 60 ⇒ true, etc.