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
(a) for all $n \in \mathbf{N}$
(b) for all n > 5
(c) for all n
(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
Hence, the correct alternative is option (c).