Sets

Find an example of sets $A$ and $B$ such that $A\cap B = \{3, 5\}$ and $A \cup B = \{2, 3, 5, 7, 8\}$.

Find an example of sets $A$ and $B$ such that $A \subseteq B$ and $A \in B$.

Recall $\Z = \{\ldots,-2,-1,0, 1,2,\ldots\}$ (the integers). Let $\Z^+ = \{1, 2, 3, \ldots\}$ be the positive integers. Let $2\Z$ be the even integers, $3\Z$ be the multiples of 3, and so on.

1. Is $\Z^+ \subseteq 2\Z$? Explain.

2. Is $2\Z \subseteq \Z^+$? Explain.

3. Find $2\Z \cap 3\Z$. Describe the set in words, and using set notation.

4. Express $\{x \in \Z \st \exists y\in \Z (x = 2y \vee x = 3y)\}$ as a union or intersection of two sets already described in this problem.

Let $A = \{a, b, c, d\}$. Find $\pow(A)$.

Find an example of sets $A$ and $B$ such that $|A| = 4$, $|B| = 5$, and $|A \cup B| = 9$.

Consider the sets $A$ and $B$, where $A = \{3, |B|\}$ and $B = \{1, |A|, |B|\}$. What are the sets?