Make the correct alternative in the following question:

Question:

Make the correct alternative in the following question:

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

(a) for all $n \in \mathbf{N}$                      

(b) for all > 5                         

(c) for all n "> 5                         

(d) for all n < 5

Solution:

As, P(5) is true and

$\mathrm{P}(k+1)$ is true whenever $\mathrm{P}(k)$ is true for all $k>5 \in \mathbf{N}$.

By the definition of the priniciple of mathematical induction, we get

P(n) is true for all n "> 5.

Hence, the correct alternative is option (c).

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