Chapter 1 Review

Chapter 1 Review #1 – 2: Write a word description of each set 1) D = {4,5,6, …} 2) A = {3,4,5,6,7} #3 – 5: Write the sets in set-builder form. (There are many correct answers.) 3) B = {2,3,4,5} 4) P = set of natural numbers between 2 and 7 inclusive 5) P = set of natural numbers between 2 and 7 exclusive #6-9: Write sets in roster form. 6) The set A of natural numbers between 2 and 5 inclusive. 7) The set A of odd natural numbers greater than or equal to 8. 9) D = {m ∈ 𝑁, 1 ≤ m < 4} 8) B = {x | x – 3 =6 } (**** The answer to problem 8 should be {9}. The answer is wrong below and it is hard to fix as it was saved as a PDF.****) #10 – 12: Find the cardinal number (n) of the following sets. That is find the number of elements in each set. 10) The set B of natural numbers between 5 and 10 exclusive. 11) The set A of natural numbers less than or equal to 7. 12) Find n(C) where C = {2,4,6,8,10,12,14} #13– 15: Determine whether the sets A and B are equal, equivalent, neither. 13) A = {4,3,2,1} B = {a,b,c,d} 14) A = {a,b,c} B = {c,b,a} 15) A = {0,1,2,3} B = {a,b,c,d,e} #16-18: Answer true or false, if false give the reason 16) Is A ⊆ B Given A = 𝑎 and B = { a,b,c} 17) Is A ⊆ B Given A= {Phoenix} and B = {Phoenix, Los Angeles, San Diego} 18) Is A ⊆ B Given A = {2,7} and B = {1,2,3,4,5} #19 – 21: Determine which of these are true. (Choose every answer that is true, in many instances there will be more than one correct choice.) A = B, A ⊆ B, 19) A = {5,7,9} B ⊆ A, A ⊂ B, B ⊂ A, or none of these B = {9, 5, 7, 3} 20) A = {𝑥|𝑥 ∈ 𝑁 𝑎𝑛𝑑 𝑥 < 3} B = {1,2} 21) A = {𝑥|𝑥 ∈ 𝑁 𝑎𝑛𝑑 𝑥 < 4} B = {3,4,5,6} #22 - 24: Find the following sets. U = {1,2,3,4,5} A = {1,2,3,4} B = {4,5} 22) A’ 23) 𝐴′ ∩ 𝐵 24) 𝐴′ ∪ 𝐵 #25 - 27: Find the following sets. U = {a,b,c,d,e} S = {a,b} T = {a,c,d} V = {a,c,e} 25) 𝑆 ∪ (𝑇 ∩ 𝑉) 26) 𝑆 ∩ (𝑉 ∩ 𝑇 ′ ) 27) (𝑉 ∩ 𝑇)′ ∪ 𝑆 #28 - 29: Sketch the region. 28) 𝐴 ∩ 𝐵′ 29) 𝐴′ ∪ 𝐵 #30 – 32: Sketch the region. 30) 𝐴 ∩ 𝐵 ∩ 𝐶′ 31) 𝐵 ∪ 𝐶 ∩ 𝐴′ #33 – 34: Use the Venn Diagram to find the following. 32) 𝐴 ∩ (𝐵 ∪ 𝐶) 33) 𝐴 ∩ 𝐵′ 34) 𝐴′ ∪ 𝐵 #35 – 36: Use the Venn Diagram to find the following. 35) 𝐴 ∩ 𝐵 ∪ 𝐶′ 36) 𝐵 ∪ 𝐶 ∪ 𝐴′ 37) A company is considering manufacturing a new flavor of yogurt. They are considering two flavors, lemon and cinnamon. In a sample of 100 people, it was found that    a) b) c) d) 70 liked lemon 60 liked cinnamon 40 liked both types Create a Venn diagram to model the information. How many liked only lemon? How many liked only cinnamon? How many liked exactly one of the two (that is they liked one but not the other)? 38) 150 students were asked which of three restaurants they have been to this year. The results of the survey were as follows: 50 have been to Olive Garden 45 have been to Oregano’s 40 have been to Outback 10 have been to both Olive Garden and Oregano’s 15 have been to both Olive Garden and Outback 20 have been to both Oregano’s and Outback 5 have been to all three a) b) c) d) e) Create a Venn diagram to model the information. How many did not go to any of the three? How many have been to Olive Garden or Oregano’s? How many have been to Outback or Oregano’s, but not Olive Garden? How many have been to exactly two of the three? Answers: 1) The set of Natural numbers greater than or equal to 4. 2) The set of Natural numbers between 3 and 7 inclusive. 3) B = { x ∈ 𝑁, 2 ≤ x ≤ 5} 4) P = { x ∈ 𝑁, 2 ≤ x ≤ 7} 5) B = { x ∈ 𝑁, 2 < x < 7} 6) {2,3,4,5} 7) {9,11,13,.. } 8) B = {9} 9) D = {1,2,3} 10) N(B) = 4 11) N(A) = 7 12) N(C) = 7 13) equivalent 14) equal and equivalent 15) neither 16) false, a is not a set 17) true 18) false, 7 is in the left set, but not in the right set 19) A ⊆ B, A ⊂ B 20) A = B, A ⊆ B, B ⊆ A 21) none 22) {5} 23) {5} 24) {4,5} 25) {a,b,c} 26) ∅ 27) {a,b,d,e} 32) 33) {1,3,5} 34) {2,4,6,7,8,9,10} 35) {2,3,4,5,8,9} 36) {1,2,4,5,6,7,8,9,10} 37a) 37b) 30 37c) 20 37d) 50 39a) 39b) 55 39c) 85 39d) 45 39e) 30