1 votes 1 votes Does the given solution is correct: When S is symmetric and transitive, if S contain (3,1),(1,3) then (3,3) should also be present form transitivity. Please verify the solution. Set Theory & Algebra engineering-mathematics ace-test-series set-theory + – Overflow04 asked Aug 23, 2022 Overflow04 546 views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Abhrajyoti00 commented Aug 23, 2022 reply Follow Share Yes (3,3) will also be present in S. But with their example, (2,1) is missing. So it is not transitive. 0 votes 0 votes Kabir5454 commented Aug 23, 2022 reply Follow Share Solution is correct . Transitive relations are not closed under union it may or may not be transitive when we union two transitive relation. Yes you are right as it is given S transitive so (3,3) will present in the S . But still $R \cup S$ is not transitive as the given argument is correct. 0 votes 0 votes [ Jiren ] commented Aug 23, 2022 reply Follow Share @GateOverflow04 Bro the Relation S is wrong because in the question they said S is symmetric and transitive but S doesnt have (3,3) pair as ( 3 S 1 ),(1 S 3 ) so according to transtive property ( 3 S 3 ) should be present 2 votes 2 votes ankitgupta.1729 commented Aug 23, 2022 reply Follow Share would (1,1) not be in S ? 3 votes 3 votes [ Jiren ] commented Aug 23, 2022 reply Follow Share @ankitgupta.1729 hi i saw some one calling you "sir” in one of the answers so im also sticking to this convention 😅 yes sir (1,1) should also be present in S because if we see the other way (1,3) (3,1) so from transitivity (1,1) should be present in S 3 votes 3 votes Please log in or register to add a comment.
4 votes 4 votes The best way to solve this question is by taking counter example EDIT : I forgot to write (a,a) in set S it's from transitive property (a,c),(c,a) so (a,a) should be present in S [ Jiren ] answered Aug 23, 2022 edited Aug 23, 2022 by [ Jiren ] [ Jiren ] comment Share Follow See 1 comment See all 1 1 comment reply Overflow04 commented Aug 23, 2022 reply Follow Share thanks you !! 0 votes 0 votes Please log in or register to add a comment.