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$1$$\newline$Lecture Notes - Section $1$.$4$- Interval Notation, Union and Intersection of Sets$\newline$Vocabulary: inequality, inclusive, set, set notation, set-builder notation, interval, interval notation, union, intersection, set of discrete elements, empty set$\newline$Objectives:$\newline$- Translate inequality symbols.$\newline$- Translate among inequality expression, number line sketch, set-builder notation, and interval notation.$\newline$- Determine the union or intersection of sets.$\newline$Objective: Translate inequality symbols.$\newline$$1$. Complete the table to translate the meaning of the inequality symbols. (See video $1.4 .1 \mathrm{in}$ the MAC$1105$C Video Library in D$2$L.)$\newline$\begin{tabular}{|c|c|c|c|}$\newline$\hline & Inequality & Meaning & Examples \\$\newline$\hline a. & $a<b$ & & $-10<0$ \\$\newline$\hline b. & $a>b$ & $a$ is $\ldots$. & $7>5$ \\$\newline$\hline c. & $a \leq b$ & $a$ is $\ldots$ or $a<b$$0$ & \begin{tabular}{l}$\newline$$a<b$$1$ \\$\newline$$a<b$$2$$\newline$\end{tabular} \\$\newline$\hline d. & $a<b$$3$ & $a$ is $\ldots$ or $a<b$$6$ & \begin{tabular}{l}$\newline$$a<b$$7$ \\$\newline$$a<b$$8$$\newline$\end{tabular} \\$\newline$\hline e. & $a<b$$9$ & & $-10<0$$0$ \\$\newline$\hline f. & $-10<0$$1$ & & \begin{tabular}{l}$\newline$$-10<0$$2$ \\$\newline$$-10<0$$3$$\newline$\end{tabular} \\$\newline$\hline g. & $-10<0$$4$ & & \begin{aligned}$-18$ & $-10<0$$5$ \\$\newline$\hline h. & $-10<0$$6$ & \begin{tabular}{l}$\newline$$-10<0$$7$ is _ $a$ and $-10<0$$9$, including both $a$ and $-10<0$$9$. \\$\newline$$-10<0$$7$ is $a$ and $-10<0$$9$, inclusive.$\newline$\end{tabular} & \begin{tabular}{c}$\newline$$a>b$$5$ \\$\newline$$a>b$$6$$\newline$\end{tabular} \\$\newline$\hline i. & $a>b$$7$ & $a$ is ___ equal to $-10<0$$9$ & $a$$0$ \\$\newline$\hline j. & $a$$1$ & $a$ is ___ equal to $-10<0$$9$ & $a$$4$ \\$\newline$\hline$\newline$\end{tabular}