26 votes 26 votes Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to $A \cup B$ $A^c \cup B^c$ $A \cap B$ $A^c \cap B^c$ Set Theory & Algebra gate1996 set-theory&algebra easy set-theory + – Kathleen asked Oct 9, 2014 • edited Jun 21, 2017 by Silpa Kathleen 6.1k views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Ashwani Kumar 2 commented Aug 27, 2019 reply Follow Share $AB'+BA'+AB$ $A(B+B')+A'B$ $A+A'B= (A+A') (A+B)= A+B$ Hence $A \cup B$ 3 votes 3 votes val_pro20 commented Dec 23, 2020 reply Follow Share why my approach is wrong ? Union taken as +,Intersection taken as *(and) A-B+B-A+AB=====AB @gatecse @Gyanu @Shashank 0 votes 0 votes Mohitdas commented Dec 6, 2021 reply Follow Share …………………………………………………………………………. 2 votes 2 votes Deepak Poonia commented Dec 16, 2022 reply Follow Share $\color{red}{\text{Find Video Solution Below:}}$ Detailed Video Solution 0 votes 0 votes Please log in or register to add a comment.
Best answer 28 votes 28 votes $(A - B) \cup (B - A) \cup (A \cap B)$ $A - B$ is A but not B. i.e. only A $B - A$ is B but not A. i.e. only B $A \cap B$ is A and B both Union of all is (only A) U (only B) U (both A and B) $= A \cup B$ Correct Answer: $A$ Digvijay Pandey answered May 31, 2015 • edited Apr 24, 2019 by Naveen Kumar 3 Digvijay Pandey comment Share Follow See all 0 reply Please log in or register to add a comment.
12 votes 12 votes We can solve it using boolean algebra also Given expression is : (A−B)∪(B−A)∪(A∩B) Which can be written in boolean algebra as AB' + BA' + AB { A-B can be expressed as A ∩B' } Which gives A+B which is nothing but A U B. Ayush Upadhyaya answered Nov 13, 2017 Ayush Upadhyaya comment Share Follow See all 0 reply Please log in or register to add a comment.
6 votes 6 votes Think like OSA: This is like the equation of HALF ADDER! (Symmetric difference= XOR) U (AB) =A XOR B + AB AND HALF ADDER GIVES SUM. SO A + B . which is A U B. :) Aspi R Osa answered Jan 9, 2016 Aspi R Osa comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments Aspi R Osa commented Jan 10, 2016 reply Follow Share sir anyways the physical significance of SUM + CARRY is the total SUM of something. and in case of SETS, i dont think a carry would have any physical significance. am i really too wrong? 1 votes 1 votes Praveen Saini commented Jan 10, 2016 reply Follow Share No, you are right btw I never guessed you can switch in btw boolean algebra and set theory as per requirement :D :/ 1 votes 1 votes Aspi R Osa commented Jan 10, 2016 reply Follow Share lack of knowledge(in me) = creativity of knowledge! :D 1 votes 1 votes Please log in or register to add a comment.
6 votes 6 votes hope it might help..... akash.dinkar12 answered Jul 22, 2017 akash.dinkar12 comment Share Follow See 1 comment See all 1 1 comment reply Puja Mishra commented Jan 21, 2018 reply Follow Share Looks like u hav mastered Venn diagram ... (y) 1 votes 1 votes Please log in or register to add a comment.