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 k > 5 $\in$ N and also P(5) is true. On the basis of this he could conclude that P(n) is true.

(a) for all n $\in$ N (b) for all n > 5 (c) for all n $\ge$ 5 (d) for all n < 5

Answer 1

As, P(5) is true and
P(k + 1) is true whenever P(k) is true for all k > 5 $\in$ N.

By the definition of the priniciple of mathematical induction, we get
P(n) is true for all n $\ge$ 5.

Hence, the correct alternative is option (c).