$\displaystyle n^2 - n + 41$ is prime (try some examples), for all n is an element of N.
Let n=1
12 - 1 + 41 = 41 is prime.
n^2 - n + 41 is not prime. so this hypothesis is not correct.
assume n^2 - n + 41 is not prime. there exist n that let n^2 - n + 41 = n^2 so n^2 - n + 41 is not prime.
therefore, when 41-n=0 this equation holds. therefore there exists a n=41 that n^2 - n + 41 is not prime.
Hence n^2 - n + 41 not true for all n is an element of N.
Is this correct?
You can't use induction here. Induction is used to prove statements for all positive integers.
Here, $\displaystyle n^2 - n + 41$ can be prime for some values of $\displaystyle n$ (such as n = 1) or not prime (such as n = 41).
To disprove a statement, all you need is just one single counterexample which I provided for you.