Problem A £2 points). Complete the definition of an equivalence relation by filling in the two blanks: A relation ~ on a set S is called an equivalence relation if 111111 •x~y⇒y~x, for all x, y ES 22 Y and Y~2⇒ for all x, y, z ES

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I need answer of :  d. Justifying your answer, find the smallest set of related pairs which must beadded to R in order for it to become an equivalence relation.

prove why they have or do not have the properties: reflexive, symmetric, antisymmetric, transitive they have. Write which of these is an equivalence relation. 1) Set A = {a,b,c}, relation R:A x A is defined as R = {(a,a},(b,b),(c,c),(a,b),(a,c),(c,b)}