91Ó°ÊÓ

Write out the following sets by listing their elements between braces. $$ \\{X: X \subseteq\\{3,2, a\\} \text { and }|X|=2\\} $$

Draw a Venn diagram for \((A-B) \cup C\).

Is \(\bigcap_{\alpha \in I} A_{a} \subseteq \bigcup_{\alpha \in I} A_{\alpha}\) always true for any collection of sets \(A_{\alpha}\) with index set \(I ?\)

Write each of the following sets by listing their elements between braces. $$ \\{x \in \mathbb{Z}:|x|<5\\} $$

Sketch these Cartesian products on the \(x-y\) plane \(\mathbb{R}^{2}\) (or \(\mathbb{R}^{3}\) for the last two). $$ \\{1,1.5,2\\} \times[1,2] $$

Sketch these Cartesian products on the \(x-y\) plane \(\mathbb{R}^{2}\) (or \(\mathbb{R}^{3}\) for the last two). $$ \\{1\\} \times[0,1] $$

Decide if the following statements are true or false. Explain. $$ \left\\{(x, y) \in \mathbb{R}^{2}: x^{2}-x=0\right\\} \subseteq\left\\{(x, y) \in \mathbb{R}^{2}: x-1=0\right\\} $$

Suppose that \(|A|=m\) and \(|B|=n .\) Find the following cardinalities. $$ |\\{X \in \mathscr{P}(A):|X| \leq 1\\}| $$

Write each of the following sets in set-builder notation. $$ \\{0,4,16,36,64,100, \ldots\\} $$

Write each of the following sets in set-builder notation. $$ \\{\ldots,-8,-3,2,7,12,17, \ldots\\} $$