Answer
See the solution.
Work Step by Step
To prove $P(1)$ is true, we will assume the antecedent is true, and prove that the consequent must also be true. So, we will use a direct proof.
$Proof.$
Assume $a$ and $b$ are positive real numbers. Then $(a+b)^1=a+b=a^1+b^1$. Hence $(a+b)^1 \geq a^1+b^1$. Thus $P(1)$ is true.$_\Box$
