Chapter 1: Problem 3
Write the following sets by listing their elements between braces. $$ \mathscr{P}(\\{\\{\varnothing\\}, 5\\}) $$
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Sketch the set \(X=[1,3] \times[1,2]\) on the plane \(\mathbb{R}^{2}\). On separate drawings, shade in the sets \(\bar{X}\) and \(\bar{X} \cap([0,2] \times[0,3])\)
List all the subsets of the following sets. $$ \\{\\{\mathbb{R}\\}\\} $$
Write the following sets by listing their elements between braces. $$ \mathscr{P}(\\{a, b\\}) \times \mathscr{P}(\\{0,1\\}) $$
List all the subsets of the following sets. $$ \\{\mathbb{R},\\{\mathbb{Q}, \mathbb{N}\\}\\} $$
Sketch the following sets of points in the \(x-y\) plane. $$ \left\\{(x, y) \in \mathbb{R}^{2}:(y-x)(y+x)=0\right\\} $$
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