Let us define a relation R on A={a,b,c,d,e}.
a) The relation R={(a,a),(b,b),(c,c),(d,d),(e,e),(a,b)} is reflexive because of (x,x)∈R for each x∈A, but it is not symmetric because of (b,a)∈/R.
b) The relation R={(a,b),(b,a)} is symmetric but not transitive because of (a,b)∈R and (b,a)∈R but (a,a)∈/R.
c) The relation R={(a,b),(b,a),(a,a),(b,b)} is transitive because of (x,y),(y,z)∈R imply (x,z)∈R, but it is not reflexive becase of (c,c)∈/R.
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