Question 7 If R is an equivalence relation on a set A, then for any a ∈ A, the set [a] is the equivalence class of a, consisting of all elements in A that are related to a by R. Note that since R is reflexive, aRa, so it is always the case that a ∈ [a].
Let A = {1,2,3,4,5,6}, and let R be the equivalence relation
R = {(1, 1), (1, 5), (2, 2), (2, 3), (2, 6), (3, 2), (3, 3), (3, 6), (4, 4), (5, 1), (5, 5), (6, 2), (6, 3), (6,6)}
(a) Determine [1]. (That is, write the set [1] = {x ∈ A: xR1} in set-roster notation.)
(b) Determine [2].
(c) Determine [3].
(d) Determine [4].