Question

A student was asked to prove a statement by induction. He proved
(i) P(5) is true and
(ii) Trutyh of P(n) $\Rightarrow$ truth of p(n + 1), n$\in$N
On the basis of this, he could conclude that P(n) is true for

• A. no n $\in$ N
• B. all n $\in$ N
• C. all n $\ge$ 5
• D. None of these

Answer 1

The correct option is C all n $\ge$ 5

If $P\left(a\right)$ is true and truth of $P\left(n\right)$ implies that $P(n+1)$ is also true, then, we can conclude that $P\left(n\right)$ is true for all $n\ge a$ where $n\in N$.
Here
$P\left(5\right)$ is true.
Hence we can conclude that $P\left(n\right)$ is true for all $n\ge 5$