Please, help to simplify set theory expression

discrete mathematicselementary-set-theory

I need to simplify set theory expression:
$ (\bar{B} \cap C) \cup \bar{D} \cup ((B \cup \bar{C}) \cap D) \cup (A \cup \bar{C} )
$

$ \bar{B} $ means not B

I understand how to solve it graphically with Euler-Venn diagram. But I got stuck with solving it analytically using standard operators such as union, intersection, difference, complement of set.

I will be so grateful if you provide your solution step by step with used properties of algebraic structure like associative and commutative laws and etc.

Best Answer

I am not using the TeX codes , sorry . I hope you can understand this handwritten version. enter image description here