Question #280874

Define a relation R on {a,b,c, int i* e . a Reflexive but not symmetric ↳ Symmetric but not transitive <> Transitive but not reflexive

1
Expert's answer
2021-12-20T11:11:37-0500

Let us define a relation RR on A={a,b,c,d,e}.A=\{a,b,c,d,e\}.


a) The relation R={(a,a),(b,b),(c,c),(d,d),(e,e),(a,b)}R=\{(a,a),(b,b),(c,c),(d,d),(e,e),(a,b)\} is reflexive because of (x,x)R(x,x)\in R for each xA,x\in A, but it is not symmetric because of (b,a)R.(b,a)\notin R.


b) The relation R={(a,b),(b,a)}R=\{(a,b),(b,a)\} is symmetric but not transitive because of (a,b)R(a,b)\in R and (b,a)R(b,a)\in R but (a,a)R.(a,a)\notin R.


c) The relation R={(a,b),(b,a),(a,a),(b,b)}R=\{(a,b),(b,a),(a,a),(b,b)\} is transitive because of (x,y),(y,z)R(x,y),(y,z)\in R imply (x,z)R,(x,z)\in R, but it is not reflexive becase of (c,c)R.(c,c)\notin R.


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