Question

Consider the following binary relations R1, R2, and R3 below, each defined over the set of integers between 0 and 4 inclusive and with each tuple (a,b) indicating that a is related to b. R1 = {(0,0), (0,3), (1, 1), (1, 2), (2,0), (2,3), (3, 1), (3,4), (4,0), (4,1)} R2 = {(1, 2), (2, 2), (3,0), (3,2), (4,0), (4,3)} R3 = {(0,0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4,4)} Which of these three relations is an equivalence relation? Select one: O a. R2 b. None of the above O c. Rī O d. R₃

Answer 1

valence delation - A relation R' on aset A is sold to be Equiluence if Ris a) Reflexive 6) symmetric c) Densible a) Reflexive relation - A relation R on a set, it is said to be reflexive if taca Caja)ER 6) symmetric xelation - A relation R on a set AS said to be symmetric if rabe Carber then Cola) ER C) Densibile: - A Relation R on a set A is sold to le Tensible if raibe, (OBER, Cb, OER ton COLCER

DR = {0,000,300D (1/2) (2,0) (23)(3/1) (3/4)04/0C40113 a) Reflexive - coo) CIR) so not in (2/2) (3/3) C4,4) missing . Carirare So finally not in Reflexine 2) R2 = {012 (12) 3,0) (3,2)(4,0) C4/33 a) Reflexie - (212) demoing co,o) LDC3304, 4) missons Reflexire mot holds good Finally not in equivaerer

3) R3 = {(oro)C1/1) (1,2)(2/1) (22 C3 824,423 a) Reflexile - Coro) C11 (22) (3,30 (4/4) the holds good 6) Symmetric (12) Card holds good onodos C) Toonsible: (12) C2,D CID holds good Anally selgesties oul condloos verooro c R3 is Equalace relation opozon * R3 is onsect bien

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