1.6 Chapter 1 Review

Chapter Review

Basic Set Concepts

  1. A ______________ is a well-defined collection of distinct objects.
  2. A collection of well-defined objects without any members in it is called the ________ _______.
  3. Write the set consisting of the last five letters of the English alphabet using the roster method.
  4. Write the set consisting of the numbers 1 through 20 inclusive using the roster method and an ellipsis.
  5. Write the set of all zebras that do not have stripes in symbolic form.
  6. Write the set of negative integers using the roster method and an ellipsis.
  7. Use set builder notation to write the set of all even integers.
  8. Write the set of all letters in the word Mississippi and label it with a capital M.
  9. Determine whether the following collection describes a well-defined set: “A group of these five types of apples: Granny Smith, Red Delicious, McIntosh, Fuji, and Jazz.”
  10. Determine whether the following collection describes a well-defined set: “A group of five large dogs.”
  11. Determine the cardinality of the set A = {Alabama, Alaska, Arkansas, Arizona}.
  12. Determine whether the following set is a finite set or an infinite set: F = {5, 10, 15, …}.
  13. Determine whether sets A and B are equal, equivalent, or neither: A = {a, b, c} and B = {1, 2, 3, 4}.
  14. Determine if sets A and B are equal, equivalent, or neither: A = {a, b, c} and B = {c, a, b}.
  15. Determine if sets A and B are equal, equivalent, or neither: A = {a, b, c} and B = {1, 2, 3}.

    Subsets

  16. If every member of set A is also a member of set B, then set A is a _________ of set B.
  17. Determine whether set A is a subset, proper subset, or neither a subset nor proper subset of set B: A = {s, o, n} and B = {s, o, n, g}.
  18. Determine whether set A is a subset, proper subset, or neither a subset nor proper subset of set B: A = {s, o, n} and B = {s, o, l}.
  19. Determine whether set A is a subset, proper subset, or neither a subset nor proper subset of set B: A = {s, o, n} and B = {o, n, s}.
  20. List all the subsets of the set {up, down}.
  21. List all the subsets of the set {0}.
  22. Calculate the total number of subsets of the set {Scooby, Velma, Daphne, Shaggy, Fred}.
  23. Calculate the total number of subsets of the set {top hat, thimble, iron, shoe, battleship, cannon}.
  24. Find a subset of the set {g, r, e, a, t} that is equivalent, but not equal, to {t, e, a}.
  25. Find a subset of the set {g, r, e, a, t} that is equal to {t, e, a}.
  26. Find two equivalent finite subsets of the set of natural numbers, N = {1, 2, 3, …}, with a cardinality of 4.
  27. Find two equal finite subsets of the set of natural numbers, N = {1, 2, 3, …}, with a cardinality of 3.

    Understanding Venn Diagrams

  28. Use the Venn diagram below to describe the relationship between the sets, symbolically and in words:
    A one-set Venn diagram is labeled E equals Elms. The union of the Venn diagram is marked U equals Trees.
    Figure 28
  29. Use the Venn diagram below to describe the relationship between the sets, symbolically and in words:
    A two-set Venn diagram not intersecting one another is given. The first set is labeled Planes while the second set is labeled Trains. The union of the Venn diagram is marked U equals Modes of Transportation.
    Figure 29
  30. Draw a Venn diagram to represent the relationship between the described sets: Falcons \subset Raptors.
  31. Draw a Venn diagram to represent the relationship between the described sets: Natural numbers \subset Integers \subset Real numbers.
  32. The universal set is the set U = {s, m, i, l, e}. Find the complement of the set E = {e, l, m}.
  33. The universal set is the set U = {1, 2, 3, …}. Find the complement of the set V = {18, 19, 20, …}.
  34. Use the Venn diagram below to determine the members of the set A′.
    A one-set Venn diagram of A shows (d, e, a, r). The union of the Venn diagram is marked U equals (r, e, a, d, i, n, g).
    Figure 34
  35. Use the Venn diagram below to determine the members of the set A′.
    A one-set Venn diagram of A shows (g, r, a, n, d). The union of the Venn diagram is marked U equals (r, e, a, d, i, n, g).
    Figure 35

    Set Operations with Two Sets

  36. What is S \cap R?
  37. What is S \cup B?
  38. Write the set containing the elements in sets B or Q.
  39. Write the set containing all the elements is both sets B and Q.
  40. Find C intersection R.
  41. Find C union R.
  42. Find the cardinality of C \cup R, n(C \cup R).
  43. Find n(S union R).
  44. Use the Venn diagram below to find A \cap B.
    A two-set Venn diagram of A and B intersecting one another is given. Set A shows d, r while set B shows f. The intersection of the sets shows a, k, e. The union of the Venn diagrams is marked (a, b, c, …, z).
    Figure 44
  45. Use the Venn diagram below to find n(A \cup B).
    A two-set Venn diagram of A and B intersecting one another is given. Set A shows 5 while set B shows 2. The intersection of the sets shows 7. Outside the intersection of Venn diagrams, 10 is marked. The union of the Venn diagram is 24.
    Figure 45

    Set Operations with Three Sets

  46. Find n(A \cup C).
  47. Find n(B \cap C).
  48. A food truck owner surveyed a group of 50 customers about their preferences for hamburger condiments. After tallying the responses, the owner found that 24 customers preferred ketchup, 11 preferred mayonnaise, and 31 preferred mustard. Of these customers, eight preferred ketchup and mayonnaise, one preferred mayonnaise and mustard, and 13 preferred ketchup and mustard. No customer preferred all three. The remaining customers did not select any of these three condiments. Draw a Venn diagram to represent this data.
  49. Given U = {r, s, t, l, n, e, i, a}, R = {r, e, s, t}, S = {s, t, a, i, r}, and L = {l, i, n, e, s}, find (S \cup R) \cap L′.
  50. Use Venn diagrams to prove that if A \subset B, then B′ \subset A′.

Attribution

Text Attribution

This text was adapted from Chapter 1 of Contemporary Mathematics, textbooks originally published by OpenStax.

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Foundations of Mathematics 12 Copyright © by imazur. All Rights Reserved.

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