Question

Give an example of a statement such that P(3) is true but P(4) is not true.

Answer 1

The required statement

P(n) : n³ + n is divisible by 3

Justification:

Put n = 3 in (i)

P(3) : (3)³ + 3 = 27 + 3 = 30, which is divisible by 3.

Put n = 4 in (i)

P(4) : (4)³ + 4 = 64 + 4 = 68, which is not divisible by 3.