(1) Consider the following relations on {1, 2, 3, 4},
Which of these relations are equivalence relations? That is which of these relations are reflexive, symmetric, and transitive
(a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3,4)}
(b) {(1, 1), (1, 2), (2, 1), (2,2), (3, 3), (4,4)}
(c) {(2, 4), (4, 2)}
(d) {(2, 1), (1, 1), (2, 2), (2, 3), (4, 4), (1, 2) (3, 2), (3, 3)}
(e) {(1, 1), (2,2), (3,3), (4,4)}
(f) {(1, 3), (1,4), (2,3), (2,4), (3,1), (3,4)}
(2) Let U={a,b,c,d,e,f,g,h,i,j,k},A={b,c,d,e,f,g},B={a,e,h,k,f}. Find
(a)Aā©B
(b)Aā”B
(c)B'
(d)A'
(e)(Aā©B)xA
(3) (a) How many integers in the set {nā Z|1⤠nā¤1100} are divisible by 2 or 5?
(b) How many integers in the set {nā Z|1⤠nā¤1100} are divisible by 2, 5, or 11?