If statement $P (n)$ is $" 3 n + 1$ is even". Then verify that statement $P (1)$ is true but $P (2)$ is not true.

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Solution

$P (n) = 3 n + 1$ even
If $n = 1$ $P (1) = 3 (1) + 1 = 4$ $P (1)$ is even
if $n = 1$ $P (2) = 3 (2) + 1 = 7$ $P (2)$ is odd
$∴ P (1)$ is true & $P (2)$ is not true.

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