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  4. A student was asked to prove a statement P(n) by induction. He proved that P(k+1) is true, whenever P(k) is true for all k>5 ∈ N and also proved that P(5) is true. On the basis of this, he could conclude that P(n) is true

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Q. A student was asked to prove a statement $P(n)$ by induction. He proved that $P(k+1)$ is true, whenever $P(k)$ is true for all $k>5 \in N$ and also proved that $P(5)$ is true. On the basis of this, he could conclude that $P(n)$ is true

Principle of Mathematical Induction

Solution:

Since, $P(5)$ is true and $P(k+1)$ is true, whenever $P(k)$ is true.