[math] \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow} \newcommand{\ddxof}[1]{\frac{d #1}{d x}} \newcommand{\ddx}{\frac{d}{dx}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\dydx}{\ddxof y} \newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}} \newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}} \newcommand{\dist}{\mathrm{distance}} \newcommand{\arccot}{\mathrm{arccot\:}} \newcommand{\arccsc}{\mathrm{arccsc\:}} \newcommand{\arcsec}{\mathrm{arcsec\:}} \newcommand{\arctanh}{\mathrm{arctanh\:}} \newcommand{\arcsinh}{\mathrm{arcsinh\:}} \newcommand{\arccosh}{\mathrm{arccosh\:}} \newcommand{\sech}{\mathrm{sech\:}} \newcommand{\csch}{\mathrm{csch\:}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\mathds}{\mathbb} [/math]

Draw each of the following subsets of [math]R[/math]. For those that are given in terms of absolute values write an alternative description that does not use the absolute value.

• Set of all [math]x[/math] such that [math]4 \lt x \leq 7.5[/math].
• Set of all [math]x[/math] such that [math]0 \lt x \lt \infty[/math].
• Set of all [math]x[/math] such that [math]5 \leq x \lt 8[/math].
• Set of all [math]x[/math] such that [math]|x| \gt 2[/math].
• Set of all [math]y[/math] such that [math]1 \lt |y| \lt 3[/math].
• Set of all [math]z[/math] such that [math]|z - 2| \leq 1[/math].
• Set of all [math]x[/math] such that [math]|x - a| \gt 0[/math].
• Set of all [math]u[/math] such that [math]1 \lt |u - 1| \lt 5[/math].