TITLE: set algebra having union and minus
QUESTION [5 upvotes]: Using algebra of sets, show that:
$$A \cup (B\setminus C) = (A \cup B)\setminus (C\setminus A)$$
I have tried using venn diagram, and they come out to be equal. Please help on proving them equal using the laws of set algebra.

REPLY [2 votes]: $A \cup (B\setminus C) = A⋃(B⋂C^c )=(A⋃B)⋂(A⋃C^c )=(A⋃B)\setminus(A⋃C^c )^c = (A⋃B)\setminus(A^c ⋂ C)=(A \cup B)\setminus (C\setminus A)$  
here $A^c=U\setminus A$: complement of A