P.S: Please present solution clearly with sound understanding and insight demonstrated (Required)

Equivalence relations Let R R be a relation such that if sin(a) = sin(b) then (a, b) . i. Verify that is an equivalence relation. ii. Give an example of 3 elements in one of the equivalence classes. iii. Consider a database of actors, e.g. on IMDB. Explain whether or not a binary relation S such that (a1, a2) S if a1 acted in the same movie as a2 is an equivalence relation (comment on all relevant properties). Use examples where appropriate.