10. Prove that for subsets X, Y, and Z of a given universal set U(a) X-Y=X-(XY)= (XUY) -Y(b) (X-Y)-Z=X - (YUZ)(c) X-(Y-Z) = (X-Y)U(Xnz)(d) (XUY) -Z=(X-Z) U(Y - Z)(e) X-(YUZ) =(x-Y)^(X-Z)Illustrate each case on a Venn diagram.

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10. Prove that for subsets X, Y, and Z of a given universal set U (a) X-Y=X-(XnY)= (XUY) - Y (b) (X-Y)-Z=X - (YUZ) (c) X-(Y-Z) = (X-Y)U(Xnz)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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Question

10. Prove that for subsets X, Y, and Z of a given universal set U
(a) X-Y=X-(XY)= (XUY) -Y
(b) (X-Y)-Z=X - (YUZ)
(c) X-(Y-Z) = (X-Y)U(Xnz)
(d) (XUY) -Z=(X-Z) U(Y - Z)
(e) X-(YUZ) =(x-Y)^(X-Z)
Illustrate each case on a Venn diagram.

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