0 votes 0 votes Prove or disprove the following: for finite sets A and B, $\overline{(A - B) \cup (B - A)} = A \cap B$ . If the proposition is incorrect, do minimal modifications to the same and prove. Set Theory & Algebra discrete-mathematics iitg-math non-gate descriptive + – dd asked Feb 22, 2017 dd 438 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Prashant. commented Feb 22, 2017 i edited by Prashant. Feb 23, 2017 reply Follow Share $\overline{(A\cap \bar{B})} \cap \overline{(B \cap \bar{A})}$ = A∩B $(\bar{A}\cup B) \cap (\bar{B} \cup A)$ = A∩B Everything without A and having B part ∩ Everything without B and having A part = A∩B Common to Both is A∩B and Everything except A and B.$\neq$ A∩B Modification : A $\cup$ B is Universe. then equation hold. 0 votes 0 votes Harsh181996 commented Feb 23, 2017 reply Follow Share can we use ven diagram to prove it ? 0 votes 0 votes Prashant. commented Feb 23, 2017 reply Follow Share yes. you can. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes If A Ս B = Universe then the proposition holds rachapalli answered Feb 23, 2017 rachapalli comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes LHS = (A∩B) U (Universe - AUB) RHS = A∩B so ...statement is incorrect .. For statement to be correct, a small modification which can be done is AUB = Universe, that is, A and B are exhaustive .. Anand Vijayan answered Feb 23, 2017 Anand Vijayan comment Share Follow See all 0 reply Please log in or register to add a comment.