Warmup¶

Q1¶

(personal questions)

Q2¶

Dana says they have 10 toys Milla says 8 toys Milla stole at least 1 toy while dana is using 1 toy

Milla: 9-17 Dana: 1-9

Q3¶

if \(C\) is the set of all students in our class today, is your group a subset or an element?¶

Subset

if \(G\) is the set of all members of your group today, what are the elements of \(G\)?¶

Each person in our group

suppose \(G\) is still the same set. how many subset of G are there?¶

possibly infinite, but currently none

What is \(G\cap C\)? \(G\cup C\)?¶

\(\cap\) represents all elements that are in both G and C (intersect) \(\cup\) represents all elements in both G and C (union)

Q4¶

Find the following cardinalities¶

• \(|A|\) when \(A=\{6,7,8,9,...,29\}\) 23 elements

• \(|A|\) when \(A=\{z\in \mathbb{Z}|-4\leq z\leq 95 \}\) 100 elements

• \(|A\cap B|\) when \(A=\{x\in \mathbb{N} |x\leq 25\}\) and \(B=\{z\in \mathbb{N}|z\) is prime\(\}\) 9 elements

Q5¶

Find a set of smallest possible size that has both \(\{1,3,5,6,10\}\) and \(\{1,2,6,8,10\}\) as subsets.¶

\(\{1,2,3,5,6,8,10\}\)

Q6¶

Let \(A=\{0,3,7,8,15\}\) and \(B=\{3,7,15\}\). How many sets \(C\) satisfy \(C\subseteq A\) and \(B\subseteq C\)?¶

\(\{3,7,15\}\) \(\{0,3,7,15\}\) \(\{3,7,8,15\}\) \(\{0,3,7,8,15\}\) 4 elements

Q7¶

Let \(A=\{1,3,5\}\) and \(B=\{2,3\}\). What are all the elements of \(A\times B\) and \(B\times A\)? Is \(A\times B=B\times A\)?¶

\(A\times B=\{(1,2),(1,3),(3,2),(3,3),(5,2),(5,3)\}\) \(B\times A=\{(2,1),(2,3),(2,5),(3,1),(3,3),(3,5)\}\) No, because the ordered pairs are not the same order

Q8¶

Draw a Venn Diagram representing the two sets \(\overline{A\cap B}\) and \(\overline{A}\cup \overline{B}\). What do you notice about \(\overline{A\cup B}\) and \(\overline{A}\cap \overline{B}\)?¶