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Question -

If P (n) is the statement “n3 +n is divisible by 3”, prove that P (3) is true but P (4) is not true.



Answer -

Given:

P (n) = n3 + n is divisible by 3

We have P (n) = n3 + n

So,

P (3) = 33 + 3

= 27 + 3

= 30

P (3) = 30, So it is divisible by 3

Now, let’s check with P (4)

P (4) = 43 + 4

= 64 + 4

= 68

P (4) = 68, so it is not divisible by 3

Hence, P (3) is true and P (4) is not true.

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