Discrete Mathematics with Graph Theory (3rd Edition) 35

Discrete Mathematics with Graph Theory (3rd Edition) 35 -...

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Section 2.2 (c) Negation: M ~ P; No converse since the statement is not an implication. (d) Negation: (M U CS) nP rzr c ; Converse: TC·~ (M U CS) n P. (e) Negation: (M U CS) n P n T =1= 0; Converse T C ~ (M U CS) n P. 12. (a) [BB] En P =1= 0 (b) OEZ, N (c) N ~ Z (d) . Z rz N (e) (P , {2}) ~ F (f) 2 E En P (g) En P = {2} 13. (a) [BB] Since A_3 ~ A3, A3 U A_3 = A3~ (b) Since A_3 ~ A3, A3 n A_ 3 = A_ 3 .. (c) A3 n (A_3)C = {a E Z 1-3 < a::; 3}= {-2,-1,0, 1,2,3}. (d) Since Ao ~ Al ~ A2 ~ A3 ~ A4, we have ni=o Ai = Ao. 33 14. [BB] Region 2 represents (AnC) ,S. Region 3 represents AnBnC; region 4 represents (AnB) ,C. 15. (a) B A . (b) i. (A U B) n C = {5, 6} ii. A, (B' A) = A = {1,2,4, 7,8,9} iii. (AUB), (AnC) = {1,2,3,4,9} iv. A EB C = {I, 2,4,7,8, 9} v. (A n C) x (A n B) = {(5, 1), (5,2), (5,4), (6, 1), (6,2), (6, 4)} 16.· (a) [BB] A ~ B, by Problem 7; (b)B·~ A, by PAUSE 4 with A and B reversed. 17.
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