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.

  • $\begingroup$ 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
  • 1
    $\begingroup$ I got U as the answer . $\endgroup$ – ADITYA PRAKASH Mar 19 at 19:09

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

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.