MCQ
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 $\text{k}>5\in\text{N}$ and also $p(5)$ is true. On the basis of this he could conclude that $p(n)$ is true.
  • A
    For all $\text{n}\in\text{N}$
  • B
    For all $n > 5$
  • For all $\text{n}\geq5$
  • D
    For all $n > 5$

Answer

Correct option: C.
For all $\text{n}\geq5$
$P(n)$ is true for all positive integer $n$,
i.e. $\text{n}\geq5,$
Where $P(n)$ is a Propositional function, complete two steps:
Basic Step : Verify that the proposition $P(1)$ is true.
Inductive Step : Show the conditional statement,
$\big[\text{P}(1) \wedge \text{P}(2) \wedge-\wedge\text{P}(\text{k})\big]\rightarrow\text{P(k+1)}$ holds for all positive integer.

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