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1 Review Test 1 Math 1332 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Write a word description of the set. 1) 1) {26, 28, 30, 32,..., 100} List the elements in the set. 2) 2) The set of the days of the week Determine if the set is the empty set. 3) 3) {x x < 6 and x > 10} Determine whether the statement is true or false. 4) 4) 17 {1, 2, 3,..., 10} Fill in the blank with either or to make the statement true. 5) 5) 49,872 the set of even natural numbers Express the set using the roster method. 6) 6) {x x N and x is greater than 13} Find the cardinal number for the set. 7) 7) {8, 10, 12,..., 66} Are the sets equivalent? 8) 8) A = {7, 8, 9, 10, 11} B = {6, 7, 8, 9, 10} Determine whether the set is finite or infinite. 9) 9) {x x N and x 100} 10) 10) {x x N and x 1000} Are the sets equal? 11) 11) A is the set of residents age 27 or older living in the United States B is the set of residents age 27 or older registered to vote in the United States Use,,, or both and to make a true statement. 12) 12) {4, 5, 6} {4, 5, 6} 1

2 Write or in the blank so that the resulting statement is true. 13) 13) {red, blue, green} {blue, green, yellow, black} Calculate the number of subsets and the number of proper subsets for the set. 1 14) 6, 1 7, 1 8, ) List all the subsets of the given set. 15) 15) {Siamese, domestic shorthair} Place the various elements in the proper regions of the Venn diagram. 16) 16) Let U = {8, 9, 10, 11, 12, 13, 14} and A = {8, 9, 12}. Find A' and place the elements in the proper region. Use the Venn diagram to list the elements of the set in roster form. 17) 17) List the elements of A. 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. 18) 18) A' Solve the problem. 19) 19) If the universal set is the set of the days of the week and set A is the set of days that begin with the letter T, write A' using the roster method. Describe A' in words. 2

3 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. 20) 20) A B' 21) 21) (A B)' 22) 22) C' A' 23) 23) C 24) 24) (A' B) (A' C') 25) 25) (B C)' A 26) 26) (A B) (A C) Use the Venn diagram to list the elements of the set in roster form. 27) 27) (A B)' Provide an appropriate response. 28) 28) The word refers to the union of sets; the word refers to the intersection of sets. 3

4 Use the Venn diagram shown to answer the question. 29) 29) Which regions represent set D F? Use the formula for the cardinal number of the union of two sets to solve the problem. 30) 30) Set A contains 5 elements, set B contains 11 elements, and 3 elements are common to sets A and B. How many elements are in A B? Solve the problem by applying the Fundamental Counting Principle with two groups of items. 31) 31) There are 5 roads leading from Bluffton to Hardeeville, 8 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon? Use the Fundamental Counting Principle to solve the problem. 32) 32) There are 9 performers who are to present their acts at a variety show. How many different ways are there to schedule their appearances? Evaluate the factorial expression. 33) 33) 9! - 5! Use the formula for n P r to solve. 34) 34) A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 9 members and any member can be elected to each position? No person can hold more than one office. In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is not necessary to solve the problem. 35) 35) One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is $100, second prize is $50, and third prize is $25, in how many different ways can the prizes be awarded? 4

5 36) 36) Five of a sample of 100 computers will be selected and tested. How many ways are there to make this selection? Use the formula for n C r to evaluate the expression. 37) 11C 3 6 C 4 37) Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 38) 38) You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card. Solve the problem. 39) 39) To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50). The order in which the selections is made does not matter. How many different selections are possible? 40) 40) In how many distinct ways can the letters in MANAGEMENT be arranged? 5

6 Answer Key Testname: UNTITLED1 1) even numbers from 26 to 100 2) {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} 3) Yes, it is the empty set. 4) True 5) 6) {14,15,16,...} 7) 30 8) Yes 9) Finite 10) Infinite 11) No 12) 13) 14) 16; 15 15) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, { } 16) A' = {10, 11, 13, 14} 17) {11, 13, 14, 17} 18) A' = {26, 27, 28,..., 40} 19) A' = {Sunday, Monday, Wednesday, Friday, Saturday}; A' is the days of the week that do not begin with the letter T. 20) {u, w} 21) {r, t, u, v, w, x, z} 22) {r, t} 23) {v, w, x, y, z} 24) {r, t, z} 25) {u} 26) {q, s, w, y} 27) {11, 12, 14, 15, 16, 18, 19} 28) or; and 29) I, II, IV, V, VI, VII 30) 13 31) ) 362,880 33) 362,760 34) ) Permutations, because the order of the prizes awarded matters. 36) Combinations, because the order of the computers selected does not matter. 37) 11 6

7 Answer Key Testname: UNTITLED1 38) ) 15,890,700 40) 226,800 7