Chapter 1: Problem 32
Find the following cardinalities. $$ |\\{\\{\\{1,4\\}, a, b,\\{\\{3,4\\}\\},\\{\varnothing\\}\\}\\}| $$
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Sketch the following sets of points in the \(x-y\) plane. $$ \\{(x, y): x \in[1,2], y \in[1,2]\\} $$
List all the subsets of the following sets. $$ \\{\\{\mathbb{R}\\}\\} $$
Find the following cardinalities. $$ |\\{x \in \mathbb{Z}:|x|<10\\}| $$
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) \(\bar{A} \times B\)
Suppose \(A=\\{4,3,6,7,1,9\\}, B=\\{5,6,8,4\\}\) and \(C=\\{5,8,4\\} .\) Find (a) \(A \cup B\) (b) \(A \cap B\) (c) \(A-B\) (d) \(A-C\) (e) \(B-A\) (f) \(A \cap C\) (g) \(B \cap C\) (h) \(B \cup C\) (i) \(C-B\)
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