Chapter 1.1, Problem 5E

### Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

Chapter
Section

### Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
3 views

# Evaluate each of the following sets, where U = { 0 , 1 , 2 , 3 , … , 10 } A = { 0 , 1 , 2 , 3 , 4 , 5 } B = { 0 , 2 , 4 , 6 , 8 , 10 } C = { 2 , 3 , 5 , 7 } . a. A ∪ B b. A ∩ C c. A ′ ∪ B d. A ∩ B ∩ C e. A ′ ∩ B ∩ C f. A ∪ ( B ∩ C ) g. A ∩ ( B ∪ C ) h. ( A ∪ B ′ ) ′ i. A − B j. B − A k. A − ( B − C ) l. C − ( B − A ) m. ( A − B ) ∩ ( C − B ) n. ( A − B ) ∩ ( A − C )

a)

To determine

The elements of set AB where the sets A and B are given by A={0,1,2,3,4,5}andB={0,2,4,6,8,10}.

Explanation

Formula Used:

If A and B are sets, the union of A and B is the set AB, given by,

AB={x|xAorxB}

Explanation:

Consider the provided sets A and B.

A={0,1,2,3,4,5} and B={0,2,4,6,8,10}

The

b)

To determine

The elements of set AC where the sets A and C are given by A={0,1,2,3,4,5}andC={2,3,5,7}.

c)

To determine

The elements of set AB where the sets A and B are given by A={0,1,2,3,4,5}andB={0,2,4,6,8,10}.

d)

To determine

The elements of set ABC where the sets A, B and C are given by A={0,1,2,3,4,5},B={0,2,4,6,8,10}andC={2,3,5,7}.

e)

To determine

The elements of set ABC where the sets A, B and C are given by A={0,1,2,3,4,5},B={0,2,4,6,8,10}andC={2,3,5,7}.

f)

To determine

The elements of set A(BC) where the sets A, B and C are given by A={0,1,2,3,4,5},B={0,2,4,6,8,10}andC={2,3,5,7}.

g)

To determine

The elements of set A(BC) where the sets A, B and C are given by A={0,1,2,3,4,5},B={0,2,4,6,8,10}andC={2,3,5,7}.

h)

To determine

The elements of set (AB) where the sets A and B are given by A={0,1,2,3,4,5}andB={0,2,4,6,8,10}.

i)

To determine

The elements of set AB where the sets A and B are given by A={0,1,2,3,4,5}andB={0,2,4,6,8,10}.

j)

To determine

The elements of set BA where the sets A and B are given by A={0,1,2,3,4,5}andB={0,2,4,6,8,10}.

k)

To determine

The elements of set A(BC) where the sets A, B and C are given by A={0,1,2,3,4,5},B={0,2,4,6,8,10}andC={2,3,5,7}.

l)

To determine

The elements of set C(BA) where the sets A, B and C are given by A={0,1,2,3,4,5},B={0,2,4,6,8,10}andC={2,3,5,7}.

m)

To determine

The elements of set (AB)(CB) where the sets A, B and C are given by A={0,1,2,3,4,5},B={0,2,4,6,8,10}andC={2,3,5,7}.

n)

To determine

The elements of set (AB)(AC) where the sets A, B and C are given by A={0,1,2,3,4,5},B={0,2,4,6,8,10}andC={2,3,5,7}.

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