question_answer

Let A = {0, 1, 2, 3} and define a relation R or A as follows R = {(0, 0)(0, 1)(0, 3)(1, 0)(1, 1)(2, 2)(3, 0)(3, 3)}. Is R reflexive, symmetric and transitive?

Answer:

Given, A = {0, 1, 2, 3} (i) R is reflexive as \[(a,\,a)\in R\,\,\forall \,\,a\in A\]             (ii) R is symmetric, as \[(0,\,1)\in R(1,\,0)\in R\] and \[(0,\,\,3)\in R\] \[\Rightarrow \] \[(3,\,\,0)\in R\] (iii) R is not transitive as \[(3,\,\,0)(0,\,\,1)\in R\] \[\Rightarrow \] \[(3,\,\,1)\notin R\]