Which of the following defined on Z is not an equivalence relation. (1) (x, y) ∈ S ⇔ x ≥ y (2) (x, y) ∈ S ⇔ x = y (3) (x, y) ∈ S ⇔ x - y is a multiple of 3 (4) (x, y) ∈ S if |x - y| is even

1) (x, y) ∈ S ⇔ x ≥ y

2) (x, y) ∈ S ⇔ x = y

3) (x, y) ∈ S ⇔ x – y is a multiple of 3

4) (x, y) ∈ S if |x – y| is even

Solution: (1)

(x, y) ∈ S ⇒ x ≥ y ⇒ y ≤ x ⇒ (y, x) ∉ S

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