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Discrete Mathematics with Graph Theory (3rd Edition) 32

# Discrete Mathematics with Graph Theory (3rd Edition) 32 -...

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30 Solutions to Exercises Exercises 2.1 1. (a) [BBJ{ -J5, J5} (b) {I, 3, 5,15, -1, -3, -5, -15} (c) [BB] {O, -~} (Although ±v'2 are solutions to the equation, they are not rational.) (d) {-1,0,1,2,3} (e) This is the empty set. There are no numbers less than -4 and bigger than +4. 2. (a) [BB] For example, 1 + i, 1 + 2i, 1 + 3i, -8 - 5i and 17 - 43i. (b) For example, {I - 2v'2, 1 - 5v'2, 1 - 7v'2, 316 - 2v'2 and 394 - 7v'2}. (c) If x = 0, y = ±5 and x/y = o. If x = 1, y = ±VU, and = ±l/VU = ±VU/24. x = 2, y = ±.J2i and = ±2.J2i/2l. Five elements of the given set are 0, VU/24, -VU/24, 2.J2i/2l and -2.J2i/2l. (d) {2, 3, 5, 6, 8}. 3. (a) [BB] {I, 2}, {I, 2, 3}, {I, 2, 4}, {I, 2, 3, 4} (b) 0, {I}, {2},{1,2} (c) 0, {I}, {2}, {3}, {4}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,3,4 },{2,3,4} (d) {3}, {4}, {1,3}, {1,4},{2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4},{1,2,3,4} ~) {1,2,3}, {1,2,4}, {1,2,3,4} (t) 0, {I}, {2}. 4. [BB] Only (c) is true. The set A contains one element, {a, b}. 5. (a) [BB] True. 3 belongs to the set {I, 3, 5}.
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