1 votes 1 votes A relation $R$ is defined as $xRy$ , if $x$ and $y$ are NOT equal. This relation $R$ is symmetric but not reflexive symmetric and transitive but not reflexive an equivalent relation none of reflexive or symmetric or transitive Set Theory & Algebra go-mathematics-1 set-theory&algebra relations + – Bikram asked Aug 6, 2016 Bikram 707 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply David commented Aug 31, 2016 i edited by Hira Thakur Nov 29, 2023 reply Follow Share I believe option is B , since it is transitive as well . Why is the answer A ? 0 votes 0 votes Bhagyashree Mahla commented Sep 5, 2016 reply Follow Share xRy and yRx then xRx so it won't be transitive 3 votes 3 votes ukn commented Jan 17, 2017 reply Follow Share Why option a is correct pls explain 1 votes 1 votes Bikram commented Jan 18, 2017 reply Follow Share @kavita_joshi xRy and yRx then xRx so it is not transitive . read this slide --> http://www3.cs.stonybrook.edu/~pfodor/courses/CSE215/L14-Relations.pdf 1 votes 1 votes Please log in or register to add a comment.
3 votes 3 votes relation hold iff x!=y 1 :for reflexive: xRx (x!=x) false ; 2: for symmetric xRy=yRx ( x!=y and y!=x ) true 3: for transitive lets : (x,y)=(1,2) (y,z) =(21) (x,z)=(11) here xRy ,yRz hold but xRx doesn't (as 1=1 ) rohit vishkarma answered Oct 5, 2017 rohit vishkarma comment Share Follow See all 4 Comments See all 4 4 Comments reply satendra commented Nov 10, 2018 reply Follow Share So , a fact can be derived that every transitive relation is reflexive also. 0 votes 0 votes JashanArora commented Dec 16, 2019 reply Follow Share @satendra That is incorrect. $A=\left \{1,2,3 \right \}$ Relation R on A = $A=\left \{(1,2) ,(2,1), (1,1) \right \}$ Transitive but not reflexive. 0 votes 0 votes dubeyprakhar commented Jul 9, 2023 reply Follow Share No it is not transitive because we have (2,1) and (1,2). Therefore we need (2,2) as well to make it Transitive. 0 votes 0 votes dubeyprakhar commented Jul 9, 2023 reply Follow Share No every Transitive relation is not always reflexive. It depends on how we have defined our relation. eg let A = {1,2,3} Let R be a relation from A to A, such that R = {(1,2), (2,1), (1,1), (2,2)} Now this relation is Symmetric and Transitive but not Reflexive. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Can't be reflexive. Symmetric, yes. Because if xRy then yRx. Transitive? Let's see. if xRy and yRz then xRz. True. if xRy and yRx then xRx... So, not transitive as xRx doesn't belong to the "not equal to" relation. Option A JashanArora answered Dec 16, 2019 JashanArora comment Share Follow See all 0 reply Please log in or register to add a comment.