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.
Answer: Option B
:
B
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B
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 ∀ n≥m
Without the base case P(m), we cannot say that P(n) is true. Hence, the statement is false.
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