Question

Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x,...

Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x, y) ∈ R if and only if x + 2 > y.

For example, (4, 3) is in R because 4 + 2 = 6, which is greater than 3.

(a) Is the relation reflexive? Prove or disprove.

(b) Is the relation symmetric? Prove or disprove.

(c) Is the relation transitive? Prove or disprove.

(d) Is it an equivalence relation? Explain.

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