Question

Please how to solve this problem! thank you

& (-76 Points) DETAILS EPPDISCMATHS 8.3.006. MY NOTES ASK YOUR TEACHER Let A = (-2,-1, 0, 1, 2, 3, 4, 5, 6, 7) and define a relation Ron A as follows: For all x,y EA, XRY 3)(x - y). It is a fact that is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [0] = [1] - [2] - (3) - How many distinct equivalence classes does R have? classes Let the distinct equivalence classes of R. (Enter your answer as a comma-separated et of sete.)

Answer 1

we seletion A = {-2,-1, 0, 1, 2, 3, 4, 5, 6, 7} defined relation R is x,y EA XRy - 31 (ex-y) are assuming the fact that this is an equivalene class of o. [o] = { YEAlony? ={LE AL 3 Icony,} = { y EA | 3k y} = {YEA | y=3k, for some keqe [0] = {0, 3,63 Class of 3 [1] = {ye Aling} = {YEAR 3 la-y ={-2,4, 4, 73 class of (2] = {QE AI Rua} = qaEA : 312-23 (2] = {-1,5,2} 3-0 is divisible by 3. [o] [3] = [0] = $ 0,3,63 0 3 No as (3] IR chas 3 distinct equivalence classes Distinct classes of R arre [o], [1], [2