Discrete Mathematics - Exam One

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}

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) ⊆/

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}

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

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 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'