   Chapter 1.1, Problem 7E

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Textbook Problem
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# Write out the power set, ℘ ( A ) , for each set A . a. A = { a } b. A = { 0 , 1 } c. A = { a , b , c } d. A = { 1 , 2 , 3 , 4 } e. A = { 1 , { 1 } } f. A = { { 1 } } g. A = { ∅ } h. A = { ∅ , { ∅ } }

a)

To determine

The power set, (A), for the set A={a}.

Explanation

The power set, (A) of a set A is the set of all possible subsets of A and is written as:

(A)={X|XA}

Consider the given set A={a}

b)

To determine

The power set, (A), for the set A={0,1}.

c)

To determine

The power set, (A), for the set A={a,b,c}.

d)

To determine

The power set, (A), for the set A={1,2,3,4}.

e)

To determine

The power set, (A), for the set A={1,{1}}.

f)

To determine

The power set, (A), for the set A={{1}}.

g)

To determine

The power set, (A), for the set A={}.

h)

To determine

The power set, (A), for the set A={,{}}.

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