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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.

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  • $\begingroup$ What is $\overline B$? Do you mean complement of $B$? $\endgroup$ – Dbchatto67 Mar 19 at 14:44
  • $\begingroup$ @Dbchatto67 It means not B $\endgroup$ – Lord of Programs Mar 19 at 16:03
  • $\begingroup$ What I got after simplification is that $A \cup B \cup C \cup {\overline {D}}.$ I think no further simplification can be made. $\endgroup$ – Dbchatto67 Mar 19 at 16:14
  • $\begingroup$ It may be universum or empty set in the end, ideally. Could you describe, your simplification step by step, please? $\endgroup$ – Lord of Programs Mar 19 at 16:24
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    $\begingroup$ I got U as the answer . $\endgroup$ – ADITYA PRAKASH Mar 19 at 19:09
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I am not using the TeX codes , sorry . I hope you can understand this handwritten version. enter image description here

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  • $\begingroup$ Thank you, it is exactly, what I need!) $\endgroup$ – Lord of Programs Mar 20 at 1:56

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