Discrete Mathematics with Graph Theory (3rd Edition) 172

Discrete - 170 Solutions to Exercises(a This part asks us for IA U B U C U D I and we have IA U B U C U D I = IAI IBI ICI IDI IA n B I IA n CI IA n

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
170 Solutions to Exercises (a) This part asks us for IA U B U C U DI and we have IA U B U C U DI = IAI + IBI + ICI + IDI - IA n BI - IA n CI - IA n DI - IB n CI - IB n DI - IC n DI + IA n B n CI + IA n B n DI + IA n C n DI + IB n C n DI -IAnBncnDI = 3333 + 2000 + 1428 + 909 - 666 - 476 - 303 - 285 - 181 - 129 + 95 + 60 + 43 + 25 - 8 = 5845. (b) This part asks for I(A n B) '-. (C U D)I = IA n BI -I(A n B) n (C U D)I· Now (A n B) n (C U D) = (A n B n C) U (A n B n D), so I(A n B) n (C U D)I = IA n B n CI + I(A n B n D)I-I(A n B n C) n (A n B n D)I = IAnBnCl + I(AnBnD)I-I(AnBnCnD)1 = 95 + 60 - 8 = 147. The answer is 666 - 147 = 519. (c) This question asks for the number of elements in ((AnBnC) '-.D) U ((AnBnD) '-.C) U ((AnCnD) '-.B) U ((BnCnD) '-.A). Since these sets are pairwise disjoint, that is, the intersection of two of the four is empty, the number of elements in the union is the sum of the elements in each set. Since I(A n B n CI '-. DI = IA n B n CI-IA n B n C n DI = 95 - 8 =
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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.

Ask a homework question - tutors are online