Let $$P(n)$$:$$n2+n+1$$ is an even integer. If $$p(k)$$ is assumed true ⇒$$P(k+1)$$ is true. Therefore, $$P(n)$$ is TRUE

Correct option is 4None of the above

Questions

Let $P (n) : n^{2} + n + 1$ is an even integer. If p(k) is assumed true $\Rightarrow P (k + 1)$ is true. Therefore, P(n) is TRUE

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for n>1

for all n∈N

for n>2

None of the above

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detailed solution

Correct option is D

Given,P(n):n2+n+1At n = 1, P(1):3, which is not an even integer. P(1 ) is not true (principle of induction is not applicable). Also, n(n + 1 ) + 1 is always an odd integer.

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Let P(n):n2+n+1 is an even integer. If p(k) is assumed true ⇒P(k+1) is true. Therefore, P(n) is TRUE

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Let $P (n) : n^{2} + n + 1$ is an even integer. If p(k) is assumed true $\Rightarrow P (k + 1)$ is true. Therefore, P(n) is TRUE