'If P(n) is a statement about natural numbers, mathematical induction may be used to prove P(n) only if P(1) is true.' State true or false.

True

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False

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Solution

The correct option is B
False

The principle of mathematical induction can be used to prove true statements P(n) about natural numbers if it is true for a specific natural number, 'm.' In this case, if proved using induction, P(n) will be true for all $n \geq m .$ 'm' need not be equal to 1.

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Similar questions

Which of the following illustrates the inductive step to prove a statement P(n) about natural numbers n by mathematical induction, where k is an arbitrary natural number?

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P (n)

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The statement P(n)

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'If P(n) is a statement about natural numbers, mathematical induction may be used to prove P(n) only if P(1) is true.' State true or false.

The correct option is B False The principle of mathematical induction can be used to prove true statements P(n) about natural numbers if it is true for a specific natural number, 'm.' In this case, if proved using induction, P(n) will be true for all n≥m. 'm' need not be equal to 1.

The correct option is B
False

The principle of mathematical induction can be used to prove true statements P(n) about natural numbers if it is true for a specific natural number, 'm.' In this case, if proved using induction, P(n) will be true for all $n \geq m .$ 'm' need not be equal to 1.