diff --git a/Misc/Warm-Ups/furniture.tex b/Misc/Warm-Ups/furniture.tex new file mode 100755 index 0000000..534d76e --- /dev/null +++ b/Misc/Warm-Ups/furniture.tex @@ -0,0 +1,150 @@ +\documentclass[ + solutions, + singlenumbering, + nopagenumber +]{../../resources/ormc_handout} +\usepackage{../../resources/macros} + + +\makeatletter +\newcommand{\thisone}{ + \if@solutions + {\color{red} $\Leftarrow$ \texttt{this one}} + \else\fi +} + +\title{Zeno's Furniture} +\uptitlel{Warm Ups} +\uptitler{\smallurl{}} +\subtitle{Prepared by Mark on \today} + +\begin{document} + + \maketitle + + Zeno Furniture sells exactly five types of furniture: + \begin{itemize} + \item Footstools + \item Hutches + \item Sideboards + \item Tables + \item Vanities + \end{itemize} + Irene buys four items, each of a different type, + and each made of exactly one kind of wood: + \begin{itemize} + \item Maple + \item Oak + \item Pine + \item Rosewood + \end{itemize} + + The following contitions govern Irene's purchases: + \begin{itemize} + \item Any vanity she buys is Maple. + \item Any rosewood item she buys is a sideboard. + \item If she buys a vanity, she does not buy a footstool. + \item If she buys a footstool, she also buys a table made of the same material. + \item Irene does not buy an oak table. + \item Exactly two of the items she buys are made of the same kind of wood. + \end{itemize} + + + + + \problem{} + Which one of the following could be an accurate + list of the items Irene buys? \par + \begin{itemize} + \item maple footstool, maple hutch, rosewood sideboard, maple table + \item oak hutch, rosewood sideboard, pine table, oak vanity + \item rosewood hutch, maple sideboard, oak table, maple vanity + \item pine footstool, rosewood sideboard, pine table, maple vanity + \item maple footstool, pine hutch, oak sideboard, maple table \thisone{} + \end{itemize} + \vfill + + + \problem{} + If Irene buys one item made of rosewood and two items made + of maple, then which one of the following pairs could be two + of the items she buys? + \begin{itemize} + \item a rosewood sideboard and an oak footstool + \item an oak hutch and a pine sideboard + \item an oak hutch and a maple table \thisone{} + \item a maple sideboard and a maple vanity + \item a maple hutch and a maple table + \end{itemize} + \vfill + \pagebreak + + + \problem{} + Which one of the following is a complete and accurate list + of all the woods any footstool that Irene buys could be made of? + \begin{itemize} + \item maple, oak + \item maple, pine \thisone{} + \item maple, rosewood + \item maple, oak, pine + \item maple, oak, pine, rosewood + \end{itemize} + \vfill + + + \problem{} + Suppose Irene buys a footstool. Then which one of the following + is a complete and accurate list of items and any one of which she + could buy in maple? + \begin{itemize} + \item footstool, hutch, sideboard, table, vanity + \item footstool, hutch, sideboard, table \thisone{} + \item footstool, hutch, sideboard + \item footstool, hutch + \item footstool + \end{itemize} + \vfill + + \problem{} + Which one of the following cannot be the two items Irene + buys that are made of the same wood as each other? + \begin{itemize} + \item footstool, hutch \thisone{} + \item hutch, sideboard + \item hutch, table + \item sideboard, vanity + \item table, vanity + \end{itemize} + \vfill + \pagebreak + + \problem{} + If Irene does not buy an item made of maple, then each of the + following must be true except... + \begin{itemize} + \item Irene buys a footstool + \item Irene buys a pine hutch \thisone{} + \item Irene buys a rosewood sideboard + \item Irene buys exactly one item made of oak + \item Irene buys exactly two items made of pine + \end{itemize} + \vfill + + + \problem{} + Suppose the condition that Irene does not buy an oak table is + replaced with the condition that she does not buy a pine table. + If all the other contitions hold as originally given, which of the + following cannot be true? + \begin{itemize} + \item Irene buys an oak footstool. + \item Irene buys a hutch and a table made of the same wood. + \item Irene buys a vanity, but she does not buy an oak table. + \item Irene buys a maple table and an oak hutch. + \item Irene buys a rosewood sideboard and exactly two items made of pine. \thisone{} + \end{itemize} + \vfill + \pagebreak + +\end{document} \ No newline at end of file