Discrete Mathematics with Graph Theory (3rd Edition) 33

# Discrete Mathematics with Graph Theory (3rd Edition) 33 -...

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Section 2.1 31 (i) True. {{I, 2}} contains just one element, {I, 2}, and this is an element of {I, 2, {I, 2}}. 8. [BB] Yes it is; for example, let x = {I} and A = {I, {I}}. 9. (a) i. {a, b, e, d} ii. [BB] {a, b, e}, {a, b, d}, {a, e, d}, {b, e, d} iii. {a,b}, {a,e}, {a,d}, {b,e}, {b,d}, {e,d} iv. {a}, {b}, {e}, {d} v.0 (b) 16 10. (a) If A = 0, then P(A) = {0} is a set containing one element, so its power set contains two elements. (b) P(A) contains two elements; P(P(A)) has four elements. 11. (a) [BB] 4; (b) [BB] 8. (c) [BB] There are 2 n subsets of a set of n elements. (See Exercise 15 in Section 5.1 for a proof.) 12. (a) [BB] False. Let A = {2}, B = {{2}l, C = {{ {2}}}. Then A is an element of B (that is, A E B) and B is an element of C (B E C), but A is not an element of C (since B is C's only element). (b) True. If x E A, then x E B since A ~ B. But since x E B, then x E C since B ~ C. (c) True. As in the previous part, we know that
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## This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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