   Chapter 1.1, Problem 10E

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# Suppose the set A has a n     elements where  n     ∈     ℤ + .a. How many elements does the power set ℘ ( A ) have?b. If 0     ≤     k     ≤     n , how many elements of the power set ℘ ( A ) contain exactly k elements?

(a)

To determine

The number of elements in power set P(A), where A has n elements and n+

Explanation

Given information:

Set A has n elements and n+.

Formula used:

1) Power set:

A power set of A, denoted by P(A), is the set of all subsets of A and is written as P(A)={X|XA}

2) Subset:

A and B be sets. A is called a subset of B if and only if every element of A is an element of B.

Explanation:

A has n elements and n+

(b)

To determine

The number of elements in power set P(A) contain exactly k elements, when 0kn

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