29 votes 29 votes Let $R$ be a symmetric and transitive relation on a set $A$. Then $R$ is reflexive and hence an equivalence relation $R$ is reflexive and hence a partial order $R$ is reflexive and hence not an equivalence relation None of the above Set Theory & Algebra gate1995 set-theory&algebra relations normal + – Kathleen asked Oct 8, 2014 • recategorized Apr 25, 2021 by Lakshman Bhaiya Kathleen 14.4k views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply !KARAN commented Dec 6, 2018 reply Follow Share Can we see this question from propositional logic point of view? $\text{R be a Symmetric and Transitive relation on a set A }$ $\implies$ $\text{R is Reflexive & Equivalence relation}$ which is completely false. It would be true if $\text{R be a Reflexive, Symmetric and Transitive relation on a set A }$ $\implies$ $\text{Equivalence relation}$ 2 votes 2 votes Punit Sharma commented Jan 12, 2019 reply Follow Share in implies R⟹E , the statement is true also if R is false... so by that way, you mean ..if ( Refl. & Symm & Transitivity ) is false than also it'll be Equivalence 0 votes 0 votes mohan123 commented Nov 2, 2019 reply Follow Share Empty relation is symmetric and transitive by default but not reflexive 1 votes 1 votes subbus commented Jun 27, 2021 i edited by subbus Jul 1, 2021 reply Follow Share @!KARAN R be a Symmetric and Transitive relation on a set A R be a Symmetric and Transitive relation on a set A ⟹⟹ R is Reflexive & Equivalence relation I think this is not the correct interpretation. The correct one will be $$\ \text{R is symmetric } \land \text{R is transitive} \to \text{R is reflexive } \to \text{ R is equivalence} $$ By Exportation Law, $$\ \text{R is symmetric } \land \text{R is transitive} \land \text{R is reflexive } \to \text{ R is equivalence} $$ 0 votes 0 votes Please log in or register to add a comment.
Best answer 42 votes 42 votes The answer is $D$. Let $A=\{1,2,3\}$ and relation $R=\{(1,2),(2,1),(1,1),(2,2)\}. R$ is symmetric and transitive but not reflexive. Because $(3,3)$ is not there. Anu answered Jun 28, 2015 • edited Apr 25, 2021 by Lakshman Bhaiya Anu comment Share Follow See all 4 Comments See all 4 4 Comments reply Ayush Upadhyaya commented Nov 10, 2017 reply Follow Share Also, the Empty relation is symmetric and transitive by default but not reflexive. Hence ans-(d) 57 votes 57 votes sujeetkumar commented Nov 24, 2019 reply Follow Share why c answer is not correct ? since R i s not reflexive therefor not equivalence it is why incorrect option? 0 votes 0 votes Aalok8523 commented Jun 23, 2020 reply Follow Share @sujeetkumar, bro please read option C carefully, it saying that R is reflexive which is not true in above question. 0 votes 0 votes taurus05 commented Apr 8, 2021 reply Follow Share Under rare circumstances i see comments with more upvotes than the original answer, mainly due to intuitive approach. Thanks ! 0 votes 0 votes Please log in or register to add a comment.
14 votes 14 votes Answer: D Let A = {(1,2),(2,1),(1,1)} A is symmetric and transitive but not reflexive as (2,2) is not there. Rajarshi Sarkar answered Jun 2, 2015 Rajarshi Sarkar comment Share Follow See all 4 Comments See all 4 4 Comments reply confused_luck commented Jan 11, 2016 reply Follow Share According to the example you have assumed, thought the answer remains correct, but you must include (2,2) into the relation as well because of transitivity. and may be you can change the set A to , A={1,2,3} 7 votes 7 votes kumar_sanjay commented Oct 14, 2016 reply Follow Share simply, take (1,1) as relation which is symmetric and transitive, but for reflexive it should have other pair ( b,b) &(c,c) if i consider set {1,2,3} hence option D 1 votes 1 votes Vishal Goel commented Jul 12, 2017 reply Follow Share The explanation is not right! 1 votes 1 votes talha hashim commented Jul 5, 2018 reply Follow Share @rajshree you must include (2,2) in your explanation 0 votes 0 votes Please log in or register to add a comment.
9 votes 9 votes here ans should be D explanation: here the relation is symmetric and transitive. if relation is symmetric and transitive then it need not necessariy be reflexive;i.e. it may or may not be reflexive. therefore ans is D jayendra answered Dec 27, 2014 jayendra comment Share Follow See all 0 reply Please log in or register to add a comment.
8 votes 8 votes We can take an empty set { } which is both symmetric and and transitive but not reflexive because diagonal elememts are not present in the set so not reflexive. Pranabesh Ghosh 1 answered Nov 27, 2016 Pranabesh Ghosh 1 comment Share Follow See all 0 reply Please log in or register to add a comment.