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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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