Exercise 1: Example : A-{ 1, 2), B= { a, b} A X B = { (1, a), (l, b), (2, a), (2, b)) Solve the following: X= {a, c} and Y= {a,b,e,f) Write down the elements of (b) Yx X (d) What could you say about two sets A and BifAx B-Bx A? Exercise 2: Consider the following relation R on the set of S of TSU students, R={(x, y) | x and y have the same major). Prove that this relation is reflexive, symmetric and transitive. Exercise 3: For all sets and relations below, state and prove that the relation is 3) Anti-Symmetric 4) Transitive a) 1) Reflexive, 2) Symmetric b) Draw the digraph of each relation the set A-(2, 3, 4, 8,12,16), and the relation R- [(a,b)| a divides b) the set B- 3,7,9, 113 and the relation R((a.b) asb) - the set X-(1,2,3,4,5) and the relation R-(a,b)1sxs3&2sys4) Exercise 4 Let X = { San Francisco, Pittsburg, Chicago, San Diego, Philadelphia, Los Angeles) Define a relation R on X as x R y if x and y are in the same state (0) Show that R is an equivalence relation (b) List the equivalence classes of X