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

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Question

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

Options

  • For all n ∈ N

  • For all n > 5

  • For all n ≥ 5

  • For all n < 5

MCQ
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Solution

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

Explanation:

Since, P(5) is true and P(k + 1) is true.

Whenever P(k) is true.

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Chapter 4: Principle of Mathematical Induction - Solved Examples [Page 69]

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NCERT Exemplar Mathematics Exemplar [English] Class 11
Chapter 4 Principle of Mathematical Induction
Solved Examples | Q 12 | Page 69

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