Discrete Mathematics - Exam One

Use the Venn diagram to list the elements of the set in roster form. [image] The set of students who studied Saturday: A) {Sam, Sophia} B) {Karen, Charly, Vijay} C) {Karen, Charly, Sam, Sophia} D) {Karen, Charly}

Either {Sam, Sophia} or {Karen, Charly, Sam, Sophia}

Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. A' ∪ B A) {q, s, t, u, v, w, x, y} B) {q, r, s, t, v, x, y, z} C) {s, u, w} D) {r, s, t, u, v, w, x, z}

Either {q, r, s, t, v, x, y, z} or {s, u, w}

Use set notation to identify the shaded region. [image] A) (A ∪ B ∪ C)' B) (A ∪ B) ∩ C' C) (A ∪ B) ∪ C' D) (A ∩ B) ∪ C'

Not (A ∪ B) ∩ C'

Find the cardinal number for the set. {8, 10, 12, ....,66} A) 30 B) 20 C) 15 D) 60

A) 30

Use the set notation to identify the shaded region. A) A ∩ B B) A ∩ B C) A - B D) A ∪ B

A) A ∩ B

Determine whether the statement is true or false. 7 ∈/ {1, 2, 3, ..., 40} A) False B) True

A) False

Use the Venn diagram show to answer the question. [image] Which region represent set D ∪ F? A) I, II, IV, V, VI, VII B) VIII C) III D) I, II, IV, V VI, VII, VIII

A) I, II, IV, V, VI, VII

Determine whether the set is finite or infinite. {x | x ∈ N and x >= 1000} A) Infinite B) Finite

A) Infinite

Calculate the number of subsets and the number of proper subsets for the set. {1/6, 1/7, 1/8, 1/9} A) 14; 15 B) 16; 15 C) 15; 14 D) 15; 16

B) 16; 15

Use the formula for the number of subsets of a set with n elements to solve the problem. Pasta comes with tomato sauce and can be ordered with some, all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli, shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for ordering pasta with tomato sauce? A) 127 B) 256 C) 255 D) 128

B) 256

Let U = {21, 22, 23, ... 40},. A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27, ...., 39}, and D = {22, 24, 26, 28, ..., 40}. Use the roster method to write the following set. A' A) A' = {26, 28, 30, ..., 40} B) A' = {26, 27, 28, ..., 40} C) A' = {21, 22, 23, ..., 40} D) A' = {27, 29, 31, ..., 39}

B) A' = {26, 27, 28, ..., 40}

Determine if the set is the empty set. {x|x is a living U.S. president born after 1700} A) Yes, it is the empty set. B) No, it is not the empty set.

B) No, it is not the empty set.

Determine if the set is the empty set. {x|x < 6 and x > 10} A) No, it is not the empty set. B) Yes, it is the empty set.

B) Yes, it is the empty set.

Use ⊆, ⊆/, or ⊂, or both ⊂ and ⊆ to make a true statement. {a, b} {z, a, y, b, x, c} A) ⊆/ B) ⊂ and ⊆ C) ⊆

B) ⊂ and ⊆

Write ⊆ or ⊆/ in the blank so that the resulting statement is true. {red, blue, green} ___ {blue, green, yellow, black} A) ⊆ B) ⊆/

B) ⊆/

Write a word description of the set: {January, February, March, April, May, June, July, August, September, October, November, December} A) Days of the year B) Seasons of the year C) Months of the Year D) Days of the Week

C) Months of the Year

Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. (A∪ B) ∩ (A∪ C) A) {q, s, w, y} B) {r, t, v, x} C) {q, s, u, w, y, z} D) {q, s, u, w, y}

C) {q, s, u, w, y, z}

Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. (A∪ B)' A) {s, u, w} B) {r, s, t, u, v, w, x, z} C) {r, t, v, x} D) {t, v, x}

C) {r, t, v, x}

Use the formula for the cardinal number of the union of two sets to solve the problem. Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A∪ B) then how many elements are in (A∪ B)? A) 8 B) 5 C) 13 D) 17

D) 17

Express the set using the roster method. {x|x ∈ N and x is greater than 13} A) {14,15,16} B) {13,14,15, ...} C) {14,16,18,...} D) {14,15,16,...}

D) {14,15,16,...}

Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. (A ∩ C)' A) {w, y} B) {q, r, s, t, u, v, w, x, y, z} C) {q, s, y, z} D) {q, r, s, t, u, v, x, z}

D) {q, r, s, t, u, v, x, z}

Express the set using set-builder notation. Use inequality notation to express the condition to express the condition x must meet in order to be a member of the set. A = {200, 201, 202, ..., 2000} A) {x | 200 < x < 2000} B) {x | x ∈ N and x >= 200} C) {x | x ∈ N and x <= 2000} D) {x | x ∈ N and 200 <= x <= 2000}

D) {x | x ∈ N and 200 <= x <= 2000}

Use the following definition to place the indicated natural number in the correct region of the Venn diagram. A palindromic number is a natural number whose value does not change if its digits are reversed. U = the set of natural numbers A = the set of palindromic numbers B = the set of odd numbers 1600 [image] A) 1600 inside III B) 1600 inside I C) 1600 inside II D) 1600 outside (left)

Either 1600 inside II or 1600 outside (left)

Place the various elements in the proper regions of the Venn diagram. Let U = {g, h, j, k, m, n} and A = {g, h, n}. Find A'. Then use a Venn Diagram to illustrate the relationship among the sets U, A, and A'. A) A' = {j, k, m} B) A' = ∅ C) A' = {g, h, m} D) A' {g, h, n}

Either A' = {j, k, m} or A' {g, h, n}

Use a Venn diagram to answer the question. A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 950 responses with the following results: 285 were interested in an interview show and a documentary, but not reruns; 38 were interested in an interview show and reruns, but not a documentary; 133 were interested in returns but not documentaries or interviews; 228 were interested in an interview show but not a documentary; 95 were interested in a documentary and reruns; 57 were interested in an interview show and reruns; 76 were interested in none of the three. How many are interested in exactly one kind of show? A) 436 B) 466 C) 456 D) 446

Not 466

Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. (A∪ B)' ∩ C A) {q, v, x} B) {v, x} C) {s, u, v, z} D) {r, w}

Not {s, u, v, z}