W WISTLIVO 3. For each part of Exercise 2, give an example of a relation on R with the desired properties. The properties of reflexivity, symmetry, and transitivity are related to the identity relation and the operations of inversion and composition. Prove that a Ris a reflexive relation on A if and only if I CR. b) Ris symmetric if and only if R = R . cRis transitive if and only if R RER 5. Let R be a relation on a set A. Prove that a if A is nonempty, the empty relation is not reflexive on A. (b) the empty relation is symmetric and transitive for every set For each of the following, prove that the relation is an equivalen Then give information about the equivalence classes as specified (a) The relation Son R given by x Sy iff x - ye Q. GI class of 0; of 1; of V2. (b) The relation R on N given by m R n iff m and n have There the tens places. Find an element of 106 that is and 30x) greater than 1000 on is an equivalence relation . Give the equivalence a n have the same digitia , between 10 the quivalence