Question

Let P(n) be some propositional function. In order to prove P(n) is true for all positive integers, n, using mathematical induction, which of the following must be proven? OP(K), where k is an arbitrary integer with k >= 1 If P(k) is true, then P(k+1) is true, where k is an arbitrary integer with k >= 1 P(O) P(k+1), where k is an arbitrary integer with k>= 1

Answer 1

Mathematical Induction is a special way of proving it contains two steps

Step 1 - Base Step :  prove it is true for initial value (initial value need not always be 1)

Step 2 - Induction Step : Assuming it is true for n=k i.e P(k) is true and prove it for n=k+1 i.e P(k+1) is true

Answer : B

A) False, we would be proving for P(k+1) and not for P(k) where K>=1

B) True, we would be proving for P(k+1) assuming P(k) is true where K>=1

C) False, initial value can't 0 because it is neither positive nor negative

D) False , Assuming P(k) is true is neccessary to prove it for P(k+1) where K>=1

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