Skip to main content
Mathematics LibreTexts

1.2.1: Exercises

  1. Last updated
  2. Save as PDF
  • Page ID
    214352

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\dsum}{\displaystyle\sum\limits} \)

    \( \newcommand{\dint}{\displaystyle\int\limits} \)

    \( \newcommand{\dlim}{\displaystyle\lim\limits} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \(\newcommand{\longvect}{\overrightarrow}\)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)

    For the following exercises, represent each set using the roster method.

    1. The set of primary colors: red, yellow, and blue.
    2. A set of the following flowers: rose, tulip, marigold, iris, and lily.
    3. The set of natural numbers between 50 and 100.
    4. The set of natural numbers greater than 17.
    5. The set of different pieces in a game of chess.
    6. The set of natural numbers less than 21.

    For the following exercises, represent each set using set builder notation.

    1. The set of all types of lizards.
    2. The set of all stars in the universe.
    3. The set of all integer multiples of 3 that are greater than zero.
    4. The set of all integer multiples of 4 that are greater than zero.
    5. The set of all plants that are edible.
    6. The set of all even numbers.

    ​​​​​For the following exercises, represent each set using the method of your choice.

    1. The set of all squares that are also circles.
    2. The set of natural numbers divisible by zero.
    3. The set of Mike and Carol’s children on the TV show, The Brady Bunch.
    4. The set of all real numbers.
    5. The set of polar bears that live in Antarctica.
    6. The set of songs written by Prince.
    7. The set of children’s books written and illustrated by Mo Willems.
    8. The set of seven colors commonly listed in a rainbow.

    For the following exercises, determine if the collection of objects represents a well-defined set or not.

    1. The names of all the characters in the book, The Fault in Our Stars by John Green.
    2. The five greatest soccer players of all time.
    3. A group of old dogs that are able to learn new tricks.
    4. A list of all the movies directed by Spike Lee as of 2021.
    5. The group of all zebras that can fly an airplane.
    6. The group of National Baseball League Hall of Fame members who have hit over 700 career home runs.

    For the following exercises, compute the cardinal value of each set.

    1. \(P = \{ {\text{Snuzzle, Butterscotch, Blue Belle, Minty, Blossom, Cotton Candy}}\} \)
    2. \(T = \{ {\text{pepperoni, sausage, bacon, ham, mushrooms, olives, bell pepper, pineapple}}\}\)
    3. \(\emptyset\)
    4. \(B = \{ 5,6,7, \ldots ,20\}\)
    5. \(F = \left\{ {\frac{1}{9},\frac{2}{9},\frac{3}{9},\frac{4}{9},\frac{5}{9},\frac{6}{9},\frac{7}{9},\frac{8}{9},\frac{9}{9}} \right\}\)
    6. \(\{ {\text{ }}\}\)
    7. \(C=\left\{n^3 \mid n\right.\) is a member of \(\left.\mathbb{N}\right\}\)
    8. \(S = \left\{ {7n|n{\text{ is an element of }}\mathbb{N}} \right\}\)
    9. \(L = \{ l,m,n, \ldots ,y\}\)
    10. The set of numbers on a standard 6-sided die.

    For the following exercises, determine whether set \(\(A\) and set \(\(B\) are equal, equivalent or neither.

    1. \(A=\{\) right, acute, obtuse \(\} ; B=\{\) equilateral, scalene, isoceles \(\}\).
    2. \(A=\left\{1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\} ; B=\left\{\frac{1}{4}, \frac{1}{3}, \frac{1}{2}, 1\right\}\).
    3. \(A=\{\) red, orange, yellow \(\} ; B=\{\) green, blue, indigo, violet \(\}\).
    4. \(A=\{5 n \mid n \in \mathbb{N}\} ; B=\mathbb{N}\).
    5. \(A=\{-2,-1,0, \ldots\} ; B=\{2,3,5, \ldots\}\).
    6. \(A=\{\) John, Paul, George, Ringo \(\} ; B=\{\) Bono, Larry, The Edge, Adam \(\}\).
    7. \(A=\emptyset ; B=\{ \}\).
    8. \(A=\{\) lemon, lime, orange \(\} ; B=\{\) orange, lemon, lime, grape \(\}\).
    For the following exercises, determine if the set described is finite or infinite.
    1. The set of natural numbers.
    2. The empty set.
    3. The set consisting of all jazz venues in New Orleans, Louisiana.
    4. The set of all real numbers.
    5. The set of all different types of cheeses.
    6. The set of all words in Merriam-Webster's Collegiate Dictionary, Eleventh Edition, published in 2020.

    1.2.1: Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

    1. Back to top
    • Was this article helpful?

    Recommended articles

    1. Article type
      Section or Page
      Show Page TOC
      no
      Transcluded
      yes
    2. Tags
      1. source[1]-math-171443