If $\displaystyle N \triangleleft G$ and $\displaystyle G/N \cong (\mathbb{Z}, +)$, show that whenever $\displaystyle H,K \leq G$ with $\displaystyle H \cap K = N $ , then either H = N or K = N

Please post a complete proof to this, so I can learn from it. Its a study question for my exam. I really appreciate it.

Thanks guys