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PRINCIPLE OF MATHEMATICAL INDUCTION — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPRINCIPLE OF MATHEMATICAL INDUCTION1 Mark
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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