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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
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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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