prove or disprove that $CL(A∩B)=CL(A)∩CL(B)$

Question

Suppose $X,τ$ a topological space. If $A$ and $B$ are any two subsets of $X$ prove or disprove that $CL(A∩B)=CL(A)∩CL(B)$

I know that closed sets is closed under intersection, however I still got the feeling that this is not true. I wonder if anyone have an counter example.

Answer 1

Try $A=[0,1)$ and $B=(1,2]$ as a counterexample.