0 votes 0 votes Set Theory & Algebra equivalence-class + – Shreya Roy asked Nov 28, 2016 Shreya Roy 622 views answer comment Share Follow See all 11 Comments See all 11 11 Comments reply Sushant Gokhale commented Dec 2, 2016 reply Follow Share answer is C? 0 votes 0 votes Shreya Roy commented Dec 3, 2016 reply Follow Share Don't know the answer :( .. What is your approach? 0 votes 0 votes Sushant Gokhale commented Dec 3, 2016 reply Follow Share Let no of elements in each equivalence class be 'n'. Now, asper handshaking theorem, there will be nP2 elemnts in the relation R corresponding to single equivalence class. Similarly , nP2 for the remaining 2 classes. So, total elements = (nP2)3 Here, in the options, only option (C) is proper cube. So, I think (C) is the answer. 0 votes 0 votes Shreya Roy commented Dec 3, 2016 reply Follow Share Did not get the Handshaing Theorem in this context .. can u plz provide any link or resources on this part? 0 votes 0 votes Sushant Gokhale commented Dec 3, 2016 reply Follow Share Handshaking means ordered pairs. Sorry, it wont be nP2. It would be n2 e.g if the equivalence class is {1,2,3} then the ordered pairs will be n2 = 32 = 9 i.e R will contain ordered pairs 1,1 2,2 3,3 1,2 2,1 2,3 3,2 1,3 3,1 Right? 0 votes 0 votes Shreya Roy commented Dec 3, 2016 reply Follow Share That's okay but did not get " total elements = (nP2)3 " 0 votes 0 votes Sushant Gokhale commented Dec 3, 2016 reply Follow Share It should be (n2)3 0 votes 0 votes Shreya Roy commented Dec 3, 2016 reply Follow Share why (n2)3 ? did not understand the cube part.. 0 votes 0 votes Sushant Gokhale commented Dec 3, 2016 reply Follow Share There are 3 equivalence classes of same size. Thts why. Read the question carefully. 0 votes 0 votes Shreya Roy commented Dec 3, 2016 reply Follow Share at least 3 equivalence class not exactly 3 is mentioned even if we consider 3 equivalence classes then total number of ordered pairs (according to your previous explanation) becomes 3*n^2 not (n2)3 0 votes 0 votes Sushant Gokhale commented Dec 3, 2016 reply Follow Share Oops...I read the question wrong. But still consider #total elements = k. n2 Now, try to find the factors of any of the answers and check if we can get a perfect square. Since, k >= 3 we can take k=4 so that we get (D) as the answer. 0 votes 0 votes Please log in or register to add a comment.