Let A = follows: For V(a,b), (c,d) € A × A, (a,b)R(c,d) a ≤ c and b
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- Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.23. Let be the equivalence relation on defined by if and only if there exists an element in such that .If , find , the equivalence class containing.For any relation on the nonempty set, the inverse of is the relation defined by if and only if . Prove the following statements. is symmetric if and only if . is antisymmetric if and only if is a subset of . is asymmetric if and only if .