A) reflexive and symmetric
B) not reflexive, but symmetric
C) symmetric and transitive, but not reflexive
D) reflexive, but not transitive
Correct Answer: C
Solution :
Given, \[x=\{a,\,b\,c,\,d,e\}\] and \[R=\{(a,\,a),\,(b,b),(c,\,c),\,(a,b),\,(b,a)\}\]. For reflexive \[(x,x)\in R,\] since \[(d,\,d)\in /\,R\] Therefore, R is not reflexive. For symmetric \[(a,b)\in R\to (b,a)\in R\] Therefore, R is symmetric. For transitive Here, \[(a,b)\,\in R\] and \[(b,a)\in R\] \[\Rightarrow \] \[(a,a)\in R\] Therefore, R is transitive. Hence, R is symmetric and transitive, but not reflexive.
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