Problem 6
List all the subsets of the following sets. $$ \\{\mathbb{R}, \mathbb{Q}, \mathbb{N}\\} $$
Problem 6
Write the following sets by listing their elements between braces. $$ \mathscr{P}(\\{1,2\\}) \times \mathscr{P}(\\{3\\}) $$
Problem 6
Write out the indicated sets by listing their elements between braces. $$ \left\\{x \in \mathbb{R}: x^{2}=x\right\\} \times\left\\{x \in \mathbb{N}: x^{2}=x\right\\} $$
Problem 6
Write each of the following sets by listing their elements between braces. $$ \left\\{x \in \mathbb{R}: x^{2}=9\right\\} $$
Problem 6
\text { Sketch the set } X=\left\\{(x, y) \in \mathbb{R}^{2}: y
Problem 6
Sketch the sets \(X=[-1,3] \times[0,2]\) and \(Y=[0,3] \times[1,4]\) on the plane \(\mathbb{R}^{2}\). On separate drawings, shade in the sets \(X \cup Y, X \cap Y, X-Y\) and \(Y-X\).
Problem 7
Sketch the sets \(X=\left\\{(x, y) \in \mathbb{R}^{2}: x^{2}+y^{2} \leq 1\right\\}\) and \(Y=\left\\{(x, y) \in \mathbb{R}^{2}: x \geq 0\right\\}\) on \(\mathbb{R}^{2}\). On separate drawings, shade in the sets \(X \cup Y, X \cap Y, X-Y\) and \(Y-X\).
Problem 7
Suppose sets \(A\) and \(B\) are in a universal set \(U\). Draw Venn diagrams for \(\overline{A \cap B}\) and \(\bar{A} \cup \bar{B}\). Based on your drawings, do you think it's true that \(\overline{A \cap B}=\bar{A} \cup \bar{B}\) ?
Problem 7
List all the subsets of the following sets. $$ \\{\mathbb{R},\\{\mathbb{Q}, \mathbb{N}\\}\\} $$
Problem 7
(a) \(\bigcup_{i \in \mathbb{N}} R \times[i, i+1]=\) (b) \(\bigcap_{i \in \mathbb{N}} \mathbb{R} \times[i, i+1]=\)
