1.4.1: Exercises
- Page ID
- 214356
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)For the following exercises, interpret each Venn diagram and describe the relationship between the sets, symbolically and in words.
For the following exercises, create a Venn diagram to represent the relationships between the sets.
All birds have wings.
All cats are animals.
All almonds are nuts, and all pecans are nuts, but no almonds are pecans.
All rectangles are quadrilaterals, and all trapezoids are quadrilaterals, but no rectangles are trapezoids.
Lizards \(\subset\) Reptiles.
Ladybugs \(\subset\) Insects.
Ladybugs \(\subset\) Insects and Ants \(\subset\) Insects, but no Ants are Ladybugs.
Lizards \(\subset\) Reptiles and Snakes \(\subset\) Reptiles, but no Lizards are Snakes.
\(A\) and \(B\) are disjoint subsets of \(U\).
\(C\) and \(D\) are disjoint subsets of \(U\).
\(T\) is a subset of \(U\).
\(S\) is a subset of \(U\).
\(J=\) Jazz, \(M=\) Music, and \(J \subset M\).
\(R=\) Reggae, \(M=\) Music, and \(R \subset M\).
\(J=\) Jazz, \(R=\) Reggae, and \(M=\) Music are sets with the following relationships: \(J \subset M, R \subset M\), and \(R\) is disjoint from \(J\).
\(J=\) Jazz, \(B=\) Bebop, and \(M=\) Music are sets with the following relationships: \(J \subset M\) and \(B \subset J\).
For the following exercises, the universal set is the set of single digit numbers, \(U=\{0,1,2,3,4,5,6,7,8,9\}\). Find the complement of each subset of \(U\).
\(A=\{6,7,8\}\)
\(A=\{0,2,4,6,8\}\)
\(A=\{ \}\)
\(A=\{0,1,4,6,8,9\}\)
\(A=\{0,1,2,3,4,5,6,7,8,9\}\)
\(A=\{0,1,3,4,5,6,7,9\}\)
\(A=\{1,2,3,4,5,6,7,8,9\}\)
\(A=\{0,3,6,9\}\)
For the following exercises, the universal set is \(U=\) \{Bashful, Doc, Dopey, Grumpy, Happy, Sleepy, Sneezy\}. Find the complement of each subset of \(U\).
\(A=\{\) Happy, Bashful, Grumpy\}
\(A=\{\) Sleepy, Sneezy \(\}\)
\(A=\{\mathrm{Doc}\}\)
\(A=\{\) Doc, Dopey \(\}\)
\(A=\emptyset\)
\(A=\{\) Doc, Grumpy, Happy, Sleepy, Bashful, Sneezy, Dopey\}
For the following exercises, the universal set is \(U=\mathbb{N}=\{1,2,3, \ldots\}\). Find the complement of each subset of \(U\).
\(A=\{1,2,3,4,5\}\)
\(A=\{1,3,5, \ldots\}\)
\(A=\{1\}\)
\(A=\{4,5,6, \ldots\}\)
For the following exercises, use the Venn diagram to determine the members of the complement of set \(A, A^{\prime}\).
