Practice Problems Week 3

You may collaborate and are encouraged to collaborate with your peers. If you do, be sure to understand the material and write it out in your own words.

There is no requirement to submit the material, but this will help you solidify the concepts.

Instructions

Let A = $ \{ x \in \mathbb N : 3 \le x \le 13\}$, B = $ \{ x \in \mathbb N: x\text{ is even } \}$, and C = $\{ x \in \mathbb N: x\{ is Odd.} \}$

a. find A $\cap$ B.

b. find A $\cup$ B.

c. Find B $\cap$ C.

d. Find B $\cup$ C.
Let A = { 1, 2, 3, 4}. Find all sets $ B \in \mathcal P (A) $
Are there sets A and B such that |A| = |B|, |A $\cup$ B| = 10, and |A $\cap$ B| = 5? Explain.
Let A = {2, 4, 6, 8}. Suppose B is a set with |B| = 5.

a. What are the smallest and largest possible values of | A $\cup$ B|? Explain your reasoning.

b. What are the smallest and largest possible values of | A $\cap$ B|? Explain your reasoning.

c. What are the smallest and largest possible values of | A $\times$ B|? Explain your reasoning.
Let A, B, and C be sets:

a. Suppose that $A \subseteq B$ and $B \subseteq C$. Does this mean that $A \subseteq C$? Prove your answer. (This is equivalent to proving that $\forall x, x \in A \to x \in C)$

b. Suppose that $A \in B$ and $B \in C$. Does this mean that $A \in C?$ Prove your answer.
In a regular deck of playing cards there are 26 red cards and 12 face cards. Explain, using sets and what you have learned about cardinalities, why there are only 32 cards which are either red or a face card.
Explain why there is no set A which satisfies A = {2, |A|}