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3.1.2.1: Exercises

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    1. Create a Venn diagram to illustrate each of the following:
      1. \((F \cap E) \cup D\)
      2. \((D \cup E)^{c} \cap F\)
      3. \(\left(F^{c} \cap E^{c}\right) \cap D\)
      4. \((D \cup E) \cup F\)
    2. Write an expression for the region outlined in red for the following Venn diagrams.
      1.  

        clipboard_e8910db6dbeb907deac79212c4844a900.png

      2.  

        clipboard_eb1180ca18b0413c87466d876f76a50fd.png

      3.  

        clipboard_e2ba153a01099bbc42e9585945b4d113d.png

      4.  

        clipboard_ed5ce75a0bf03631442611dbd9e68f2de.png

    3. Let \(A=\{1,2,3,4,5\} \quad B=\{1,3,5\} \quad C=\{4,6\}\). Find the cardinality of the given set.
      1. \(\mathrm{n}(A)\)
      2. \(\mathrm{n}(B)\)
      3. \(\mathrm{n}(A \cup C)\)
      4. \(\mathrm{n}(A \cap C)\)
      5. \(\mathrm{n}(B \cap C)\)
    4. The Venn diagram here shows the cardinality of each region in the diagram. Use this to find the cardinality of each given set.

      clipboard_ec18bbe27affa8adec9600536fe3a9d5b.png

      1. \(\mathrm{n}(A \cap C)\)
      2. \(\mathrm{n}(B \cup C)\)
      3. \(\mathrm{n}\left(A \cap B \cap C^{c}\right)\)
      4. \(\mathrm{n}\left(A \cap B^{c} \cap C\right)\)
    5. If \(n(G)=20, n(H)=30, n(G \cap H)=5,\) find \(n(G \cup H)\)
    6. If \(n(G)=5, n(H)=8, n(G \cap H)=4,\) find \(n(G \cup H)\)
    7. A survey was given asking people whether they watch movies at home from Netflix, Hulu, or Amazon. Use the results to determine how many people use Redbox.

      \(\begin{array}{ll} \text{52 only use Netflix} & \text{62 only use Hulu} \\ \text{24 only use Amazon} & \text{16 use only Amazon and Hulu} \\ \text{48 use only Netflix and Hulu} & \text{30 use only Amazon and Netflix} \\ \text{10 use all three} & \text{25 use none of these} \end{array}\)

    8. A survey asked buyers whether color, size, or brand influenced their choice of cell phone. The results are below. How many people were influenced by brand?

      \(\begin{array}{ll} \text{5 said only color} & \text{8 said only size} \\ \text{16 said only brand} & \text{20 said only color and size} \\ \text{42 said only color and brand} & \text{53 said only size and brand} \\ \text{102 said all three} & \text{20 said none of these} \end{array}\)

    9. Use the given information to complete a Venn diagram, then determine: a) how many students have seen exactly one of these movies, and b) how many had seen only Star Wars.

      \(\begin{array}{ll} \text{18 had seen The Matrix (M)} & \text{24 had seen Star Wars (SW)} \\ \text{20 had seen Lord of the Rings (LotR)} & \text{10 had seen M and SW} \\ \text{14 had seen LotR and SW } & \text{12 had seen M and LotR} \\ \text{6 had seen all three} & \text{} \end{array}\)

    10. A survey asked people what alternative transportation modes they use. Using the data to complete a Venn diagram, then determine: a) what percent of people only ride the bus, and b) how many people don’t use any alternate transportation.

      \(\begin{array}{ll} \text{30% use the bus} & \text{20% ride a bicycle} \\ \text{25% walk} & \text{5% use the bus and ride a bicycle} \\ \text{10% ride a bicycle and walk} & \text{12% use the bus and walk} \\ \text{2% use all three} & \text{} \end{array}\)

    This page titled 3.1.2.1: Exercises is shared under a CC BY-SA license and was authored, remixed, and/or curated by Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia.