25 votes 25 votes Let $E, F$ and $G$ be finite sets. Let $X = (E ∩ F) - (F ∩ G)$ and $Y = (E - (E ∩ G)) - (E - F)$. Which one of the following is true? $X ⊂ Y$ $X ⊃ Y$ $X = Y$ $X - Y ≠ \emptyset$ and $Y - X ≠ \emptyset$ Set Theory & Algebra gatecse-2006 set-theory&algebra normal set-theory + – Rucha Shelke asked Sep 17, 2014 • edited Mar 26, 2021 by soujanyareddy13 Rucha Shelke 6.7k views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments Tuhin Dutta commented Dec 18, 2017 reply Follow Share Let $E\ =\ \{ \ 1,2,3,4,5,6,7,8,9,10\ \},\ F\ =\ \{\ 5,10\ \},\ G\ =\ \{\ 2,4,6,8,10\ \}\\E\ \cap\ F\ =\ \{\ 5,10\ \}\\F\ \cap\ G\ =\ \{\ 10\ \}\\X\ =\ \{\ 5\ \}\ \\E\ \cap\ G\ =\ \{\ 2,4,6,8,10\ \}\\E\ -\ E\ \cap\ G\ =\ \{ \ 1,3,5,7,9\ \}\\E\ -\ F\ =\ \{\ 1,2,3,4,6,7,8,9\}\\Y\ =\ (E\ -\ (E\ \cap\ G\ ))\ -\ (E\ -\ F) =\ \{\ 5 \ \}\\ \therefore\ X\ = \ Y. So\ answer\ is\ (C)$ Note that this example also eliminates all the other options. 1 votes 1 votes subbus commented May 27, 2021 reply Follow Share For these type of questions, this method seems simple and fast 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.
3 votes 3 votes X=(E∩F)−(F∩G) Y=(E−(E∩G))−(E−F) Let E={1,2,3,4,5} positive integers F={2,3,5,7} prime numbers G={1,3,5} odd numbers E∩ F ={2,3,5} ,F∩G={3,5} so X={2} E∩G={1,3,5} ,E-{E∩G}={2,4},E-F={1,4} Y={2} so X and Y are same so option C is right Rishi yadav answered Aug 27, 2017 Rishi yadav comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes As the question gives options into the hands of student: So, CASE 1 not equal to CASE 2. CASE 1 => X=Y CASE 2 => X, not equal Y and X is a subset of Y. So what should be chosen? And why we presumption for all set merger and there must be an intersection point. yarunsharma answered Jun 9, 2020 yarunsharma comment Share Follow See 1 comment See all 1 1 comment reply Ritik_Sindhwani__ commented May 18, 2021 reply Follow Share y is phi 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes BEST METHOD the solution can be obtained for boolean algebra as follows: X=(E∩F)−(F∩G) =EF−FG =EF∩(FG)′ =EF.(F′+G′) =EFF′+EFG′ =EFG′ Similarly, Y=(E−(E∩G))−(E−F) =(E−EG)−(E.F′) =E.(EG)′−EF′ =E.(E′+G′)−EF′ =EG′−EF′ =EG′.(EF′)′ =EG′.(E′+F) =EE′G′+EFG′ =EFG′ Therefore, X=Y akshay_123 answered Sep 26, 2023 akshay_123 comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Option C is Correct. i_m_sudip answered Apr 4 i_m_sudip comment Share Follow See all 0 reply Please log in or register to add a comment.