Question

For questions 16-18, what are the equivalence classes. Pls say how many eqivalence classes are for each.

Thank you in advance, but completed with in the hour would be greatly apreciated bc I have an exam, and I will obviously like any completed work. Hope you all have a great day!

Example. Let R-{(a, b) E Z x Ζ : lal-lol}, for era mple: 2R-2) and 4R4 but 43. We see that R is an equivalence relation on Z. First, since la|-la. for all a E Z, R is reflexive. Next, to see R is symmetric, let a, b e Z and suppose that aRb. Then jao Z and that aRb and bRe, then and hence lb)- la, thus bRa. Finally, suppose that a, b,c we know: therefore lal = ld and ale. Therefore R is transitive and an equivalence relation. Rb if a and b are fans of the same team. o assume, reasonably I hope, that no one can be a fan of two different teams. Question 16. On the set of soccer fans, define a Show that R is an equivalence relation. Question 17·Consider the relation R = {(a, b) E Z x Z : a, b have the same parity )Show that R is an equivalence relation. Question 18. Prove that the relation S on R gitven by aSu if and only if -veQ s an equvalencé retation - y E Q as an

Answer 1

公 l6 16 Yelah on . 0 om ahs aRb s, th hm.her喽equivolhu duses are the thi one

AW ete. Thure ae in For e etc.