Define the following relation R in the set X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. For integers x, y ∈ X, let xRy if and only if x^2 - y^2 or x^2 + y^2 is divisible by 10. Prove that R is an equivalence relation and determine the equivalence classes of R.

From the options below, select the ones which are true for the relation ~ on the set of real numbers that is defined by x ~ y if x ≤y. is an equivalence relation O~ is reflexive ~ is transitive O ~ is symmetric ONone of the above

3. Let R be a relation defined on the set A = N × N where (a, b) R (c, d) if að = cd. Show R is an equivalence relation. Then, list the elements of the equivalence class [(9, 2)].

5) What is the cardinality of the set {characters in set A}? 6) Let X = {strings in A}. Find |X 7) Let X {strings in A} Name two B, CC X and two D, ECX such that... a) BUC X B = C = b) DNE #Ø E = 8) Suppose we define a relation on the set {strings in A} by making 69°F a