Discrete Mathematics with Graph Theory (3rd Edition) 34

# Discrete Mathematics with Graph Theory (3rd Edition) 34 -...

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32 Solutions to Exercises Exercises 2.2 1. (a) [BB] A = {I, 2, 3,4,5, 6}. B = {-I, 0,1,2,3,4, 5}, C = {O, 2, -2}. (b) AU C = {-2,0, 1, 2,3,4,5,6}. B n C = {0,2}, B" C = {-I, 1,3,4, 5}. A EI1 B = {-1,6,0}, C x (B n C) = {(O, 0), (0,2), (2,0), (2,2), (-2,0), (-2, 2)}, (A" B) " C = {6}, A " (B " C) = {2, 6}, (B U 0) n {0} = 0. (c) S = {(I, -1), (2,0), (3, 1), (4,2), (5, 3), (6, 4)}; T = {(I, 2), (2, 2)}. 2. (a) [BB] S n T = {v'2, 25}. S U T = {2, 5, v'2, 25,11", ~,4, 6, n, T x (S n T) = {(4, v'2), (4,25), (25, v'2), (25,25), (v'2, v'2), (v'2,25),(6,v'2),(6,25),(~,v'2),(~,25)}. (b) [BB] Z U S = {v'2, 11",~, 0,1, -1, 2, -2, ... }; Z n S = {2, 5, 25}; Z UT = {v'2, ~,O, 1, -1,2, -2, ... }; Z nT = {4,25,6}. (c) Z n (S U T) = {2, 5, 25, 4, 6} = (Z n S) U (Z n T). The two sets are equal. (d) Z U (S nT) = {v'2,0, 1, -1,2, -2, ... } = Zu {v'2} = (ZU S) n (Z U T). The two sets are equal. , 3. (a) [BB] {I, 9, 0, 6, 7}; (b) {4, 6, 5}; (c) {O, I}. 4. A
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