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In this paper, we study a problem of non-constant entire function $ f $ thatshares a set $ \mathcal{S}=\{a,b,c\} $ with its $ k $-th derivative $ f^{(k)}$, where $ a, b $ and $ c $ are any three distinct complex numbers. We havefound a gap in the statement of the main result of \textit{Chang-Fang-Zalcman}\cite{Cha & Fan & al-ADM-2007} and with some help of the method used by\textit{Chang-Fang-Zalcman}, we have generalized the result of\textit{Chang-Fang-Zalcman} in a more compact form. As an application, wegeneralize the famous Br$\ddot{u}$ck conjecture \cite{Bru-1996} with the ideaof set sharing.

Set shared by an entire function with its $k$-th derivatives using normal families