Problem 5
Draw Venn diagrams for \(A \cup(B \cap C)\) and \((A \cup B) \cap(A \cup C)\). Based on your drawings, do you think \(A \cup(B \cap C)=(A \cup B) \cap(A \cup C) ?\)
Problem 5
(a) \(\bigcup_{i \in \mathbb{N}}[i, i+1]=\) (b) \(\bigcap_{i \in \mathbb{N}}[i, i+1]=\)
Problem 5
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.)
Problem 5
Write out the indicated sets by listing their elements between braces. $$ \left\\{x \in \mathbb{R}: x^{2}=2\right\\} \times\\{x \in \mathbb{R}:|x|=2\\} $$
Problem 5
List all the subsets of the following sets. $$ \\{\varnothing\\} $$
Problem 5
Sketch the set \(X=\left\\{(x, y) \in \mathbb{R}^{2}: 1 \leq x^{2}+y^{2} \leq 4\right\\}\) on the plane \(\mathbb{R}^{2} .\) On a separate drawing, shade in the set \(\bar{X}\).
Problem 5
Write each of the following sets by listing their elements between braces. $$ \left\\{x \in \mathbb{R}: x^{2}=3\right\\} $$
Problem 5
Write the following sets by listing their elements between braces. $$ \mathscr{P}(\mathscr{P}(\\{2\\})) $$
Problem 6
(a) \(\bigcup_{i \in \mathbb{N}}[0, i+1]=\) (b) \(\bigcap_{i \in N}[0, i+1]=\)
Problem 6
List all the subsets of the following sets. $$ \\{\mathbb{R}, \mathbb{Q}, \mathbb{N}\\} $$
