0 votes 0 votes What are Binary Relations ? How many of them possible on a set of N elements ? Rohan Mundhey asked Oct 12, 2016 Rohan Mundhey 455 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply mcjoshi commented Oct 12, 2016 i edited by mcjoshi Oct 12, 2016 reply Follow Share A relation is a subset of cross product of elements. Binary relation on a set of $N$ elements means total subsets of cross product of A*A, which is $2^{N^2}$. 2 votes 2 votes Digvijay Pandey commented Oct 12, 2016 reply Follow Share ^^ no of element is A*A is n^2 so no of relation will be 2^n^2 2 votes 2 votes Rohan Mundhey commented Oct 12, 2016 reply Follow Share But why is it called Binary ? It's a set of subsets......what makes it Binary ? is it just a name or there is more to it ? 0 votes 0 votes Digvijay Pandey commented Oct 12, 2016 reply Follow Share Binary because it is relation from one set to other set. Here no of sets are two so it is binary relation. 0 votes 0 votes Rohan Mundhey commented Oct 12, 2016 reply Follow Share But here the other set is the SAME set . A X A = n^2 therefore , no of subsets = 2^ n2 1 votes 1 votes vivek9837 commented Oct 12, 2016 reply Follow Share Relations mean sets of ordered pairs. In case of of two sets A and B it is a subset of product set A × B If |A| = m and |B| = n Then the possible subset of A × B is 2mn 0 votes 0 votes Please log in or register to add a comment.