Question

For each of the following relations R: (i) Determine which of the three properties (reflexive, symmetric, transitive) R satisfies. Justify your responses. (ii) If R is an equivalence relation, determine the equivalence classes of R. (a) R = {(x, y) ? ? × ? | |x ? y| ? 1} (b) R = {(a, b) ? ? × ? | a ?? b}

          For each of the following relations R:
(i) Determine which of the three properties (reflexive, symmetric, transitive) R satisfies. Justify your responses.
(ii) If R is an equivalence relation, determine the equivalence classes of R.
(a) R = {(x, y) ? ? × ? | |x ? y| ? 1}
(b) R = {(a, b) ? ? × ? | a ?? b}

For each of the following relations R:
(i) Determine which of the three properties (reflexive, symmetric, transitive) R satisfies. Justify your responses.
(ii) If R is an equivalence relation, determine the equivalence classes of R.
(a) R = (x, y) ? ? × ? | |x ? y| ? 1
(b) R = (a, b) ? ? × ? | a ?? b

Added by Natalia G.

Calculus: Early Transcendentals

James Stewart 8th Edition

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For each of the following relations R: (i) Determine which of the three properties (reflexive, symmetric, transitive) R satisfies. Justify your responses. (ii) If R is an equivalence relation, determine the equivalence classes of R. (a) R = {(x,y) ∈ ℝ × ℝ | |x − y| ≤ 1} (b) R = {(a,b) ∈ ℤ × ℤ | a ≡₃ b}