Draw a “bag diagram” similar to what we did in Example on page to illustrate each set, A,...

Draw a “bag diagram” similar to what we did in Example on page to illustrate each set, A, before finding its cardinal number.

Finding the Cardinal Number of a Set

State whether each set is finite or infinite. If it is finite, state its cardinal number using n(A) notation.

a) P = {x : x is a planet in our solar system}

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b) N = {1, 2, 3, c}

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c) A = {y : y is a person living in the United States who is not a citizen}

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d) ∅

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e) X = {{1, 2, 3}, {1, 4, 5}, {3}}

SOLUTION:

a) There are eight planets; therefore, this is a finite set. n(P) = 8.

b) The set of counting numbers is an infinite set.

c) There are a finite number of people living in the United States who are not citizens; however, we probably do not know n(A).

d) The empty set has no elements, so it is a finite set. Thus, n(∅) = 0.

e) If you consider the given bag diagram, you can easily see that the set X contains three objects: the set {1, 2, 3}, the set {1, 4, 5}, and the set {3}. Therefore, n(X) = 3.

{{1, 2}, {1, 2, 3}}