Q.

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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a

for n>1

b

for all n∈N

c

for n>2

d

None of the above

answer is D.

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Detailed Solution

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