14. For a,b E Z, define a ~ b if and only if 4a + b is a multiple of 5. Show that defines an equivalence relation on Z. What is the equivalence class 0?

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

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Let S be a nonempty subset of Z and let R be a relation defined on S by xRy if 3 | (x + 2y). If S = {−7, −6, −2, 0, 1, 4, 5, 7}, then what are the distinct equivalence classes in this case? Please show how you find them

The relation R on the set of all integer numbers is defined by (x, y) = R_if and only if |x| = [y]. Then, R is an equivalence relation. True False

8. Let A be a set of nonzero integers and let R be a relation on A × A defined by (a, b)R(c, d) whenever ad = bc. Show that R is an equivalence relation. That is, R is reflexive, symmetric, and transitive.