MAT 119 6.1 Sets & Set Operations

# MAT 119 6.1 Sets & Set Operations

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TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. List the elements of the set in roster notation. (Enter for the empty set.)

{x | x is a letter in the word HIPPOPOTAMUS}

1. List the elements of the set in roster notation. (Enter for the empty set.)

{x | 4 ? x = 5 and x is an integer}

1. State whether the statements are true or false.

(a) B

(b) B B

1. State whether the statements are true or false.

(a) { = /p>

(b) {b, h} {b, h, j}

1. Let A = {3, 5, 8, 11, 16}. Determine whether the statements are true or false.

(a) 0 A

(b) {3, 8, 16} A

1. Let A = {a, e, l, t, r}. Which of the following sets are equal to A? (Select all that apply.)

{x | x is a letter of the word latter }

{x | x is a letter of the word later }

{x | x is a letter of the word rated }

{x | x is a letter of the word relate }

{x | x is a letter of the word late }

1. Find the smallest possible set (i.e., the set with the least number of elements) that contains the given sets as subsets. (Enter your answer using roster notation. Enter for the empty set.)

{1, 2}, {1, 3, 6}, {6, 7, 10, 12}

1. Let U denote the set of all students who applied for admission to the freshman class at Faber College for the upcoming academic year and let

A = {x U | x is a successful applicant}

B = {x U | x is a female student who is enrolled in the freshman class}

C = {x U | x is a male student who is enrolled in the freshman class}

(a)Use Venn diagrams to represent the sets U, A, B, and C. (Label the answer blanks with the correct letters.)

(b)Determine whether the following statements are true or false.

(i)A B

(ii)B A

(iii)C B

1. Check the boxes in the accompanying figures to indicate which regions should be shaded to represent each set. (Select all that apply.)

(a) A Bc

(b) Ac ? B

1. Let

U = {?8, ?6, ?3, 1, 4, 6, 11, 13, 15, 20},

A = {?8, ?3, 4, 11, 15},

B = {?6, 1, 6, 13, 20},

and

C = {?8, ?6, 1, 4, 13, 15}.

Find each set. (Enter for the empty set.)

(a) (A ? B) C

(b) (A B C)c

(c) (A ? B ? C)c

1. Determine whether the pairs of sets are disjoint.

(a) {?10, ?2, 5}

(b) {?6, 1, 7, 11}, {?10, ?6, 12, 19}

1. Let U denote the set of all employees at Universal Life Insurance Company, and let

T = {x U | x drinks tea}

C = {x U | x drinks coffee}.

Describe each set in words.

(a)

T C

The set of all employees at the Universal Life Insurance Company who drink tea and do not drink coffee.

The set of all employees at the Universal Life Insurance Company who drink tea and coffee.

The set of all employees at the Universal Life Insurance Company who do not drink tea and drink coffee.

The set of all employees at the Universal Life Insurance Company who drink tea and/or coffee.

The set of all employees at the Universal Life Insurance Company who do not drink tea and/or coffee.

(b)

T ? C

The set of all employees at the Universal Life Insurance Company who drink tea and do not drink coffee.

The set of all employees at the Universal Life Insurance Company who drink tea and coffee.

The set of all employees at the Universal Life Insurance Company who do not drink tea and drink coffee.

The set of all employees at the Universal Life Insurance Company who drink tea and/or coffee.

The set of all employees at the Universal Life Insurance Company who do not drink tea and/or coffee.

1. Let U denote the set of all senators in Congress and let

D = {x U | x is a Democrat}

R = {x U | x is a Republican}

F = {x U | x is a female}

L = {x U | x is a lawyer}.

Write the set that represents each statement.

(a) The set of all Democrats who are female or are lawyers

(b) The set of all senators who are not Democrats or are lawyers

1. Refer to the accompanying figure and list the points that belong to each set. (Enter for the empty set.)

(a) A ? (B C)

(b) (B ? C)c

MAT 119
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Excerpt from file: 1. List the elements of the set in roster notation. (Enter for the empty set.) {x x is a letter in the word HIPPOPOTAMUS} x { H,I,P,O,T,A,M,U,S } 2. List the elements of the set in roster notation. (Enter for the empty set.) {x 4 x 5 and x is an integer} x {-1} 3. State whether the

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