Let P(n) denote the statement that n^2 + n is | vedclass

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(D) The statement $P(n)$ is $n^2 + n$ is odd.We can write $n^2 + n = n(n + 1)$.Since $n$ and $n + 1$ are consecutive integers,one of them must be even

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None of these

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(D) The statement $P(n)$ is $n^2 + n$ is odd.We can write $n^2 + n = n(n + 1)$.Since $n$ and $n + 1$ are consecutive integers,one of them must be even and the other must be odd.The product of an even number and an odd number is always even.Therefore,$n^2 + n$ is always even for all natural numbers $n$.Since the statement claims $n^2 + n$ is odd,the statement $P(n)$ is false for all $n \in \mathbb{N}$.Thus,there is no $n$ for which $P(n)$ is true.Hence,the correct option is $(d)$.

Let $P(n)$ denote the statement that $n^2 + n$ is odd. It is seen that $P(n) \Rightarrow P(n + 1)$. $P(n)$ is true for all:

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