If Pn is statement such that P3 is true- Assuming Pk is true - Pk-1 is true for all k - 2- then Pn is true-

The correct option is B For n ≥ 3 Given P (3) is true.Assume P(k) is true ⇒ P(k+1) is true means if P(3) is true ...

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Standard XII

Mathematics

Proof by mathematical induction

If Pn is st...

Question

If $P (n)$ is statement such that $P (3)$ is true. Assuming P(k) is true $\Rightarrow$ $P (k + 1)$ is true for all $k$ $\geq$ $2$ , then $P (n)$ is true.

For all

n

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For

n

\geq

3

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For

n

\geq

4

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None of these

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Solution

The correct option is B For $n$ $\geq$ $3$
Given $P (3)$ is true.
Assume $P (k)$ is true $\Rightarrow$ $P (k + 1)$ is true means if $P (3)$ is true $\Rightarrow$ $P (4)$ is true $\Rightarrow$ $P (5)$ is true and so on. So statement is true for all $n \geq 3$ .

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Q. Make the correct alternative in the following question:

A student was asked to prove a statement P(n) by induction. He proved P(k +1) is true whenever P(k) is true for all k > 5

\in

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(a) for all n

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The statement P(n) is

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If P(n) is statement such that P(3) is true. Assuming P(k) is true ⇒ P(k+1) is true for all k ≥ 2, then P(n) is true.

The correct option is B For n ≥ 3Given P(3) is true.Assume P(k) is true ⇒ P(k+1) is true means if P(3) is true ⇒ P(4) is true ⇒ P(5) is true and so on. So statement is true for all n≥3.

If $P (n)$ is statement such that $P (3)$ is true. Assuming P(k) is true $\Rightarrow$ $P (k + 1)$ is true for all $k$ $\geq$ $2$ , then $P (n)$ is true.

The correct option is B For $n$ $\geq$ $3$
Given $P (3)$ is true.
Assume $P (k)$ is true $\Rightarrow$ $P (k + 1)$ is true means if $P (3)$ is true $\Rightarrow$ $P (4)$ is true $\Rightarrow$ $P (5)$ is true and so on. So statement is true for all $n \geq 3$ .