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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Determine whether each of the following is either A , A , U , or , where A is an arbitrary subset of the universal set U .

a. A A b. A A
c. A A d. A A
e. A f. A
g. A U h. A U
i. U A j. A
k. l. U
m. ( A ) n. A

a)

To determine

Whether the expression, ‘AA’ is either A, A, U, or .

Explanation

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

AB={x|xAorxB}

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

AB={x|xAorxB}

The complement A of A is given by,

A=UA={xU|

b)

To determine

Whether the expression, ‘AA’ is either A, A, U, or .

c)

To determine

Whether the expression, ‘AA’ is either A, A, U, or .

d)

To determine

Whether the expression, ‘AA’ is either A, A, U, or .

e)

To determine

Whether the expression, ‘A’ is either A, A, U, or .

f)

To determine

Whether the expression, ‘A’ is either A, A, U, or .

g)

To determine

Whether the expression, ‘AU’ is either A, A, U, or .

h)

To determine

Whether the expression, ‘AU’ is either A, A, U, or .

i)

To determine

Whether the expression, ‘UA’ is either A, A, U, or .

j)

To determine

Whether the expression, ‘A’ is either A, A, U, or .

k)

To determine

Whether the expression, ‘’ is either A, A, U, or .

l)

To determine

Whether the expression, ‘U’ is either A, A, U, or .

m)

To determine

Whether the expression, ‘(A)’ is either A, A, U, or .

n)

To determine

Whether the expression, ‘A’ is either A, A, U, or .

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