Exercise 1: Example: A -(, 2), B f a, b) AX B ((, a), (1, b). (2, a). 2, b) Solve the following X; {a, c} and Y-(a, b, e, f). Write down the elements of (a) Xx Y- (d) What could you say about two sets A and BifA B-Bx 47 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 a) 1) Reflexive, 2) Symmetric 3) Anti-Symnmetric 4) Transitive b) Draw the digraph of each relation - the set A (2, 3, 4, 8,12,16;, and the relation R- ((a,b)l a divides b) - the set B- {3,7,9, 11) and the relation R ((a,b)l a s b) the set X (1,.2,3,4,5) and the relation R-(ab)l 1Ss3&2 sys4 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 (a) Show that R is an equivalence relation (b) List the equivalence classes of X