If P(n) is the statement “n3 + n is divisible by 3”, prove that P(3) is true but P(4) is not true.
Given. P(n) = n3 + n is divisible by 3
Find P(3) is true but P(4) is not true
We have P(n) = n3 + n is divisible by 3
Let’s check with P(3)
= P(3) = 33 + 3
= P(3) = 27 + 3
Therefore P(3) = 30, So it is divisible by 3
Now check with P(4)
= P(4) = 43 + 4
= P(4) = 64 + 4
Therefore P(4) = 68, So it is not divisible by 3
Hence, P(3) is true and P(4) is not true.