1. Find two sets A and B such that BE A and BC A. 2. Can you conclude that A =B if A, B, and C are sets such that (i) A-C B-C and (ii) A+ C = BOC 10 10 10 Give reason. 3. For the following sub-problems, fill in the blanks with the appropriate 10 relationship chosen from the list lacnone]. You should choose the relationship which must be true, not just one which can be true. AU(BOC) (AUC) (AUB) 4. Determine whether f: ZxZ-Z is onto for the following cases if a) f (m, n) |m|+|n| 10 b) f(m, n) m n Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (4, 2)} on the set {1, 2, 3, 4) that is reflexive, symmetric and transitive. 10 6. Find S R for the following R and S. 10 R=(((1,3), (2, 4), (3, 1), (3,2)), and S=((2, 1), (3, 1), (4, 1)) 7. Suppose that R1 and R2 are symmetric relations on a set A. Is R1 U R2 also 10 symmetric? Is R1 R2 also symmetric? Explain. 8. Give a transitive relation on the set (m, n, o, p) and contain (m, n) and (n, p). 10