Exam 7: Sets and Counting

Find how many outcomes are possible for the decision algorithms. Alternative 1 Alternative 2 Step 1: six outcomes Step 1: three outcomes Step 2: two outcomes Step 2: two outcomes Step 3: two outcomes

Find how many outcomes are possible for the decision algorithms. Step 1 Step 2 Alternative 1:1 outcome Alternative 1:1 outcome Alternative 2: 1 outcome Alternative 2:1 outcome Alternative 3:2 outcomes

Professor Oger must choose between an extra writing assignment and an extra reading assignment for the upcoming spring break. For the writing assignment, there are 4 essay topics to choose from and three different mandatory lengths (30 pages, 35 pages, or 40 pages). The reading topic would consist of one scholarly biography combined with one volume of essays. There are 4 biographies and four volumes of essays to choose from. How many choices does she have

How many eight-letter sequences are possible that use the letters f, i, t, t, i, n, g, s

List the elements of all outcomes of rolling two indistinguishable dice such that the numbers add up to 6.

The following table shows the amount spent, in billions of dollars, on recreational boats and accessories in the United States during the period 1999-2001. (Let S be the set of all dollars represented in the table.) Compute the cardinality of the set described as $n ( A \cap ( N \cup U ) )$ . Used Boats, New Boats, Accessories, Total , 5 7 3 15 , 7 7.5 2 16.5 , 8 8 5 21 Total 20 22.5 10 52.5 ​ ​ $n ( A \cap ( N \cup U ) ) =$ __________ billion dollars.

Use Venn Diagrams to determine which of the following identities are true for the subsets B, D, and G of T.

Let A =\{ June, Jill, Molly, Lucy \} B =\{ Jill, Lucy, Jane \} C =\{ Rachel, Jill, Lucy \} Find the set $A \cup C$ .

Let ​ A=\{ Janet, Justine, Solly, Lucy \} B=\{ Justine, Lucy, Jennifer \} C=\{ Ruth, Justine, Lucy \} ​ Find the set $A \cup C$ .

A freelance computer consultant keeps a database of her clients, which contains the names ? $S = \{ \text { Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert } \}$ . ? The following clients owe her money: ? $N = \{ \text { Hilbert, Crafts, Effigy, Global } \}$ . ? The following clients have done at least $10,000 worth of business with her: ? $B = \{ \text { Hilbert, Brothers, Crafts, Dion } \}$ ? Write the clients who owe her money and have done at least $10,000 worth of business with her. ? The answer is __________.

Evaluate $C ( 9,6 )$ .

A bag contains 3 red marbles, 5 blue marbles, 3 yellow marbles, and 2 lavender marbles. How many sets of 3 marbles include none of the yellow marbles

A freelance computer consultant keeps a database of her clients, which contains the names S = {Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert}. The following clients owe her money: $N = \{ \text { Hilbert, Crafts, Effigy, Global } \}$ The following clients have done at least $10,000 worth of business with her: $B = \{ \text { Hilbert, Brothers, Crafts, Dion } \}$ Find the clients who owe her money and have done at least $10,000 worth of business with her.

The following table shows the results of a survey of authors by a fictitious publishing company. New Authors Established Authors Total Successful 6 24 30 Unsuccessful 13 58 71 Total 19 82 101 Consider the following subsets of the set S of all authors represented in the table: C, the set of successful authors; U, the set of unsuccessful authors; N, the set of new authors; and E, the set of established authors. Find the number of elements that set $C \cap N ^ { \prime }$ contains.

Your favorite restaurant offers a total of 11 desserts, of which 9 have ice cream as a main ingredient, and 8 have fruit as a main ingredient. Assuming that all of them have either ice cream or fruit or both as a main ingredient, how many have both ?

How many eight-letter sequences are possible that use the letters p, r, o, p, e, r, t, y

Some written languages, such as Chinese and Japanese, use tens of thousands of different characters. If a language uses 4,096 characters, a computer code for this language would have to use how many bits (1 or 0) per character ?

If $n ( A ) = 40$ , $n ( B ) = 21$ , and $n ( A \cap B ) = 3$ , find $n ( A \cup B )$ . ​ $n ( A \cup B ) =$ __________

If $n ( A ) = 62$ , $n ( B ) = 24$ , and $n ( A \cap B ) = 5$ , find $n ( A \cup B )$ . ​ $n ( A \cup B ) =$ __________

If $n ( A ) = 110$ , $n ( A \cup B ) = 180$ , and $n ( A \cap B ) = 45$ , find $n ( B )$ .