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Which of these relations on the set of integers is reflexive ? O R2 = {(a, b) i a -b or a = -b} O R4 = {(a, b) l a +bs3} O RI = {(a, b) | a > b} O R3 = {(a, b) I a =b+ 1} Which of these relations on (0, 1, 2, 3} are equivalence relations? O {(0, 0), (1, 1), (1, 2). (2, 1), (2. 2). (3, 3)} O {(0, 0). (0. 1). (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 2), (3, 3)} (0, 0), (1, 1), (1, 3),(2, 2). (2, 3), (3, 1). (3, 2), (3, 3)} {(0, 0), (0, 2), (2, 0), (2, 2). (2, 3), (3, 2), (3, 3)}

Which of these relations on the set of integers is reflexive ? O R2 = {(a, b) i a -b or a = -b} O R4 = {(a, b) l a +bs3} O RI = {(a, b) | a > b} O R3 = {(a, b) I a =b+ 1} Which of these relations on (0, 1, 2, 3} are equivalence relations? O {(0, 0), (1, 1), (1, 2). (2, 1), (2. 2). (3, 3)} O {(0, 0). (0. 1). (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 2), (3, 3)} (0, 0), (1, 1), (1, 3),(2, 2). (2, 3), (3, 1). (3, 2), (3, 3)} {(0, 0), (0, 2), (2, 0), (2, 2). (2, 3), (3, 2), (3, 3)}

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 18E: Let R be the relation defined on the set of integers by aRb if and only if ab. Prove or disprove...
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Which of these relations on the set of integers is reflexive ? O R2 = {(a, b) l a =b or a = -b} O R4 = {(a, b) l a +bs3} O RI = {(a, b) l a > b} O R3 = {(a, b) I a = b + 1} %3D %3! Which of these relations on {0, 1, 2, 3} are equivalence relations? o {(0, 0), (1, 1). (1, 2), (2, 1), (2. 2). (3, 3)} O {(0, 0). (0. 1). (0, 2), (1, 0), (1. 1), (1, 2), (2, 0), (2, 2), (3, 3)} O {(0,0), (1, 1), (1, 3).(2, 2). (2, 3), (3, 1). (3, 2), (3, 3)} o {(0, 0), (0, 2). (2 0), (2. 2). (2 3), (3. 2), (3, 3)}
Transcribed Image Text:Which of these relations on the set of integers is reflexive ? O R2 = {(a, b) l a =b or a = -b} O R4 = {(a, b) l a +bs3} O RI = {(a, b) l a > b} O R3 = {(a, b) I a = b + 1} %3D %3! Which of these relations on {0, 1, 2, 3} are equivalence relations? o {(0, 0), (1, 1). (1, 2), (2, 1), (2. 2). (3, 3)} O {(0, 0). (0. 1). (0, 2), (1, 0), (1. 1), (1, 2), (2, 0), (2, 2), (3, 3)} O {(0,0), (1, 1), (1, 3).(2, 2). (2, 3), (3, 1). (3, 2), (3, 3)} o {(0, 0), (0, 2). (2 0), (2. 2). (2 3), (3. 2), (3, 3)}
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