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311MExam1Review

# 311MExam1Review -...

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\documentclass[12pt]{report} %\usepackage[T1]{fontenc} %\usepackage{times} \usepackage{amsthm} \input{amssymb.sty} %\usepackage{amssymb} \usepackage{amscd,amsmath} \usepackage[arrow, matrix]{xy} \evensidemargin -0.15in \oddsidemargin -0.15in %\textwidth 6in %\textheight 8in \textwidth 6.8in \textheight 9.0in \topmargin -.5in \begin{document} \begin{center} {\bf 311M Review Problems for Midterm Exam}\\ %{\bf Due Monday, October 4. }\\ \end{center} \begin{enumerate} \item Negate the following statements: \begin{enumerate} \item Kate is 21 and red-haired. \item $\exists x \in \mathbb{R}$ such that $\forall y \in \mathbb{R}$, $xy = 0$. \item For every $x \in \mathbb{Q}$, it is impossible to find $y \in \mathbb{R}$ such that $xy = 0$ or $x + y = 12$. \end{enumerate} \item Write down the contrapositives of the following statements. \begin{enumerate} \item If $x \neq 0$, then Bob is your uncle. \item If $A \subset B$, then $A \cap B \neq \emptyset$. \item If $x \not\in A \cap B$, then $x \not\in A$ or $x \not\in B$. \end{enumerate}

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