MAT – 106 – G1 Homework Spring 2021

MAT – 106 – G1 Homework Spring 2021 Name____________________________________________________________________ Date:__________________________ Identify the set as finite or infinite. 1) {10, 11, 12, . . ., 40} 2) {x|x is a fraction between 84 and 85} 3) The set of fractions that are less than 1 but greater than 0 4) The set of natural numbers greater than 100 Express the set in roster form. 5) {x|x is a whole number between 1 and 5} 6) The set of all whole numbers greater than 6 and less than 10 7) The set of integers greater than 0 and less than 4 Write the set in set-builder notation. 8) {2, 4, 6, 8} 9) {15, 16, 17, 18} 1 Find n(A) for the set. 10) A = {6, 8, 10, 12, 14} 11) A = {x | x is a month in the year} 12) A = {x∣x ∈ N and 15 ≤ x ≤ 23} Determine whether the sets are equal, equivalent, both, or neither. 13) {brake} and {break} 14) {2, 15} and {2, 1, 5} Let A = {1, 3, 5, 7} B = {5, 6, 7, 8} C = {5, 8} D = {2, 5, 8} U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the statement is true or false. 15) D ⊆ B 16) {5} ⊆ D 17) { } ⊂ C Use ⊆ , ⊈ , ⊂ , or both ⊂ and ⊆ to make a true statement. {5, 6, 7, 8} 18) {6, 7, 8} 2 19) {a, b} {z, a, y, b, x, c} 20) {x | x ∈ N and x > 8} {x | x ∈ N and 4 < x ≤ 8} List all subsets or determine the number of subsets as requested. 21) Determine the number of subsets of {mom, dad, son, daughter} 22) Determine the number of subsets of {1, 2, 3, …, 6} If the statement is true for all sets C and D, write ʺtrue.ʺ If it is not true for all sets C and D, write ʺfalse.ʺ Assume that C ∅ , U ≠ ∅ , and C ⊂ U. 23) C ⊆ U 24) ∅ ⊆ ∅ For the given sets, construct a Venn diagram and place the elements in the proper region. 25) Let U = {c, d, g, h, k, u, q} A = {d, h, g, q} B = {c, d, h, u} 3 ≠ 26) Let U = {d, e, j, i, m, n, r} A = {e, j, i, n} B = {d, e, j, r} Let U = {all soda pops}, A = {all diet soda pops}, B = {all cola soda pops}, C = {all soda pops in cans}, and D = {all caffeine-free soda pops}. Describe the set in words. 27) A ∩ B ∩ D 28) (A ∩ B) ∩ Cʹ 29) (A ∪ D) ∩ Cʹ Use the Venn diagram to list the set of elements in roster form. 30) Find (A ∪ B)ʹ. 7 x q 5 1 f 4 Construct a Venn diagram illustrating the following sets. 31) U = {2, 4, 6, 8, 10, 12} A = {2, 6, 10} B = {2, 4, 8} C = {2, 8, 10, 12} 32) U = {a, b, c, d, e, f, g, h, i,j , k, l, m, n, o, p} A = {a, e, i, o} B = {b, c, d, f, g, h, j, k, l, m} C = {a, b, c, d, e, f, g} Use Venn diagrams to determine whether the following statements are equal for all sets A and B. 33) (A ∪ B)ʹ, Aʹ ∪ Bʹ 5 34) (A ∪ B)ʹ, Aʹ ∪ Bʹ Solve the problem. 35) Monticello residents were surveyed concerning their preferences for candidates Moore and Allen in an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen, 100 support both Moore and Allen, and 250 support only Moore. How many residents support Moore or Allen? 36) 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 600 responses with the following results: 180 were interested in an interview show and a documentary, but not reruns. 24 were interested in an interview show and reruns but not a documentary 84 were interested in reruns but not an interview show. 144 were interested in an interview show but not a documentary. 60 were interested in a documentary and reruns. 36 were interested in an interview show and reruns. 48 were interested in none of the three. How many are interested in exactly one kind of show? 6 37) A survey of 142 college students was done to find out what elective courses they were taking. Let A = the set of those taking art, B = the set of those taking basketweaving, and C = the set of those taking canoeing. The study revealed the following information. n(A) = 45 n(A ∩ B) = 12 n(B) = 55 n(A ∩ C) = 15 n(C) = 40 n(B ∩ C) = 23 n(A ∩ B ∩ C) = 2 How many students were not taking any of these electives? 38) Results of a survey of fifty students indicate that 30 like red jelly beans, 29 like green jelly beans, and 17 like both red and green jelly beans. How many of the students surveyed like no green jelly beans? 7
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