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Questions about the branch of algebra that deals with groups.

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Is $K\cap \langle H\cup N\rangle‎\subseteq‎ \langle H\cup (K\cap N)\rangle$? [closed]

If $G$ is a arbitrary group, $H,K,N\leq G$ such that $H‎\subseteq‎ K$, then $K\cap \langle H\cup N\rangle‎\subseteq‎ \langle H\cup (K\cap N)\rangle$?. If it is not true, how can I find an counterexamp …
Jamal Farokhi's user avatar