Consider the statement " $\mathrm{P}(n): n^2-n+37$ is prime." then, which one of the following is true?
Consider the statement " $\mathrm{P}(n): n^2-n+37$ is prime." then, which one of the following is true?
$\mathrm{P}(3)$ is false, but $\mathrm{P}(5)$ is true.
$P(5)$ is false, but $P(3)$ is true.
Both $\mathrm{P}(3)$ and $\mathrm{P}(5)$ are true.
Both $\mathrm{P}(3)$ and $\mathrm{P}(5)$ are false.
Solution
"p $(n): n^2-n+37$ is prime"
Now, $\mathrm{p}(3)=3^2-3+37=43$ (which is prime)
and $p(5)=5^2-5+37=57$ (which is not prime)
Hence, $\mathrm{p}(3)$ is true but $\mathrm{p}(5)$ is false
In the question write ' $n$ ' ' in place of ' $n_2$ '