8 (Z, u Z2 u Z3)n Z = Ø.Let Z1, Z2, Z3y and Z, be non-emipty sets.(a) Find a single example for the four sets so that all four of the following properties aretrue at the same time. Be clear and make.sure vou specifysuch example exists, clearly state so and explain why.i. (Z u Z2) c Z4.ii. (Z2 u Z3) c Z4.iii. Vi + je {1,2,3}, Z; n Z; = Ø.are indeed true. If nostrackt, cA(b)there a relationship that you can specify between the four sets Z1, Z2. Z3, andス。。く。

This is the problem of set theory.

(a) Find a single example for the four sets so that all four of the following properties are true at the same time. Be clear and make.sure vou specify the Universe of discourse. Illustrate, using your example, that each of the properties are indeed true. If no such example exists, clearly state so and explain why. i. (Z1u Z2) c Z4. ii. (Z2 u Z3) c Z4. iii. Vi + je {1,2,3}, Z¡ n Z; = Ø. iv. (Z, u Z2 U Za)n Z = 0. (b) Is there a relationship that you can specify between the four sets Z1, Z2. Z3, and くな、。 acolate.

(a) Find a single example for the four sets so that all four of the following properties are true at the same time. Be clear and make.sure vou specify the Universe of discourse. Illustrate, using your example, that each of the properties are indeed true. If no such example exists, clearly state so and explain why. i. (Z1u Z2) c Z4. ii. (Z2 u Z3) c Z4. iii. Vi + je {1,2,3}, Z¡ n Z; = Ø. iv. (Z, u Z2 U Za)n Z = 0. (b) Is there a relationship that you can specify between the four sets Z1, Z2. Z3, and くな、。 acolate.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...

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