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Question

'For all natural numbers N, if P(n) is a statement about n and P(k+1) is true if P(k) is true for an arbitrary natural number k, then P(n) is always true.' State true or false.


  1. False

  2. True


Solution

The correct option is A

False


For the proof by mathematical induction to work, the statement P(n) must be true for a specific instance of a natural number.

Hence, if P(m) is true, where m is a specific natural number and P(k+1) is true if P(k) is true for an arbitrary natural number k, then, P(n) is true  nm

Without the base case P(m), we cannot say that P(n) is true. Hence, the statement is false.

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