If `P(n)` is the statement `n^2+n` is even, and if `P(r)` is true then `P(r+1)` is

Options

A. True
B. False
C. Not determined
D. None of these

Answer

A

Explanation

Given as `P (n) = n^2 + n` is even and `P (r)` is true,
now `r^2 + r` is even

Let us considering `r^2 + r = 2k … (i) `


Then, `(r + 1)^2 + (r + 1)`


`=r^2 + 1 + 2r + r + 1 `

`=(r^2 + r) + 2r + 2 `

...