25 votes 25 votes Let $A, B$ and $C$ be non-empty sets and let $X = ( A - B ) - C$ and $Y = ( A - C ) - ( B - C ).$ Which one of the following is TRUE? $X = Y$ $X ⊂ Y$ $Y ⊂ X$ None of these Set Theory & Algebra gatecse-2005 set-theory&algebra easy set-theory + – gatecse asked Sep 21, 2014 • edited Jun 21, 2017 by Silpa gatecse 7.0k views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply krishn.jh commented Jul 6, 2018 reply Follow Share @Akash Kanase or some one Please comment on below: 0 votes 0 votes Shubhgupta commented Jul 21, 2018 reply Follow Share @krishn.jh, B-C should be {2}. It will always be equal. 2 votes 2 votes krishn.jh commented Jul 22, 2018 reply Follow Share Yeah i did mistake there ok yes it will be always equal :) @ Shubhgupta thank you 0 votes 0 votes Mohitdas commented Dec 8, 2021 reply Follow Share ……………………………………………………… 1 votes 1 votes Please log in or register to add a comment.
Best answer 37 votes 37 votes $X = (A-B) - C = {1,4} - {4,5,6,7 } = 1$ $Y = (A-C) -(B-C) = {1,2} - {2,3} = 1$ So, $X = Y$. Answer $A$ Akash Kanase answered Nov 28, 2015 • edited May 14, 2019 by Pooja Khatri Akash Kanase comment Share Follow See all 6 Comments See all 6 6 Comments reply habedo007 commented Aug 25, 2017 reply Follow Share That's the simple distributive law: $P*(Q \bigstar R)=(P*Q)\bigstar(P*R)$ 1 votes 1 votes Prateek kumar commented Jan 13, 2018 reply Follow Share yes X= Y here is shaded area :- 1 votes 1 votes yashpaneliya commented Mar 25, 2021 reply Follow Share Can X ⊆ Y or Y ⊆ X be the answer of this question? 1 votes 1 votes Deepak Poonia commented Apr 23, 2022 reply Follow Share $\color{red}{\text{Find Video Solution Below, solved by 3 different methods:}}$ Detailed Video Solution 1 votes 1 votes ritiksri8 commented Mar 17 reply Follow Share Best way 0 votes 0 votes i_m_sudip commented Apr 4 reply Follow Share I have also solved this in the same way. 0 votes 0 votes Please log in or register to add a comment.
19 votes 19 votes X=(A-B)-C =>AB' - C =>AB'C' Y=(A-C)-(B-C) =>AC'-BC' =>AC'(B+C') =>AC'B' so X=Y note:P-Q is equivalent to P intersection Q' or P-Q=PQ' Bhagirathi answered Jan 17, 2016 Bhagirathi comment Share Follow See 1 comment See all 1 1 comment reply rawan commented Jan 9, 2019 reply Follow Share This should be the accepted answer. Also, there's a slight mistake. It should be $AC'(B'+C)$ instead of $AC'(B+C')$ in the second-last step of Y 0 votes 0 votes Please log in or register to add a comment.
11 votes 11 votes From the venn diagram it is clear that, X=Y (Option A) Ayush Upadhyaya answered Apr 21, 2017 • reshown Apr 13, 2018 by Ayush Upadhyaya Ayush Upadhyaya comment Share Follow See all 0 reply Please log in or register to add a comment.
5 votes 5 votes we can also check by taking any three random sets Prateek kumar answered May 3, 2017 Prateek kumar comment Share Follow See all 0 reply Please log in or register to add a comment.