Question 12 Marks

If $P(n)$ is the statement " $n^3+n$ is divisible by 3 ", prove that $P(3)$ is true but $P(4)$ is not true.

Answer

$P(n): n^3+n$ is divisible by $3 P(3): 3^3+3$ is divisible by $3 \Rightarrow P(3): 30$ is divisible by $3 \therefore P(3)$ is true. Now, $P(4): 4^3+3=$ 67 is divisible by 3 Since, 67 is not divisible by 3 So, $P(4)$ is not true.

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