Chapter 1: Problem 34
Find the following cardinalities. $$ \mid\\{x \in \mathbb{N}:|x|<10\\} $$
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Sketch the sets \(X=[1,3] \times[1,3]\) and \(Y=[2,4] \times[2,4]\) on the plane \(\mathbb{R}^{2}\). On separate drawings, shade in the sets \(X \cup Y, X \cap Y, X-Y\) and \(Y-X .\) (Hint: \(X\) and \(Y\) are Cartesian products of intervals. You may wish to review how you drew sets like \([1,3] \times[1,3]\) in the exercises for Section 1.2.)
Write the following sets by listing their elements between braces. $$ \mathscr{P}(\\{\\{a, b\\},\\{c\\}\\}) $$
Write the following sets by listing their elements between braces. $$ \mathscr{P}(\\{a, b\\}) \times \mathscr{P}(\\{0,1\\}) $$
For each \(n \in \mathbb{N},\) let \(A_{n}=\\{-2 n, 0,2 n\\}\) (a) \(\bigcup_{i \in \mathbb{N}} A_{i}=\) (b) \(\bigcap_{i \in \mathbb{N}} A_{i}=\)
Let \(A=\\{0,2,4,6,8\\}\) and \(B=\\{1,3,5,7\\}\) have universal set \(U=\\{0,1,2, \ldots, 8\\} .\) Find: (a) \(\bar{A}\) (b) \(\bar{B}\) (c) \(A \cap \bar{A}\) (d) \(A \cup \bar{A}\) (e) \(A-\bar{A}\) (f) \(\overline{A \cup B}\) (g) \(\bar{A} \cap \bar{B}\) (h) \(\overline{A \cap B}\) (i) \(\bar{A} \times B\)
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