   Chapter 1.1, Problem 6E

Chapter
Section
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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