Answered: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9,…

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, a, b, c, d, e}. If A = {1, 2, a, e} and B = {1, 2, 3, 4, a, b, c}, find the following. (a) n(Ac) (b) n(A ∩ Bc) (c) n(A ∪ Bc) (d) n(Ac ∩ Bc)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.1: Sets

Problem 37E: Prove or disprove that AB=AC implies B=C.

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Let

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, a, b, c, d, e}.

A = {1, 2, a, e}

and

B = {1, 2, 3, 4, a, b, c},

find the following.

(a)

n(A^c)

(b)

n(A ∩ B^c)

(c)

n(A ∪ B^c)

(d)

n(A^c ∩ B^c)

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