Lesson 1
Practice Problem Set 1 - Solutions

1. $A{\displaystyle \cup B=\left\{5,6,7\right\}}{\displaystyle \cup \left\{1,2,3,4,6\right\}}=\left\{1,2,3,4,5,6,7\right\}$

2. $A{\displaystyle \cap C=\left\{5,6,7\right\}{\displaystyle \cap \left\{8,9,10\right\}}}=$$\varnothing$
These sets share no elements, so the intersection is empty.

3. $\left(A{\displaystyle \cup C}\right){\displaystyle \cap B}$
First, create $A{\displaystyle \cup C}$.
$A{\displaystyle \cup C}=\left\{5,6,7\right\}{\displaystyle \cup \left\{8,9,10\right\}}=\left\{5,6,7,8,9,10\right\}$
Next, intersect this new set with the set B.
$\left(A{\displaystyle \cup C}\right){\displaystyle \cap B}=\left\{5,6,7,8,9,10\right\}{\displaystyle \cap \left\{1,2,3,4,6\right\}}=\left\{6\right\}$

4. $B{\displaystyle \cap D=\left\{1,2,3,4,6\right\}}{\displaystyle \cap \left\{1,7,9\right\}}=\left\{1\right\}$

5. $\left(A{\displaystyle \cap B}\right){\displaystyle \cup \left(C{\displaystyle \cap D}\right)}$
First create $\left(A{\displaystyle \cap B}\right)$, then create $\left(C{\displaystyle \cap D}\right)$.
$\left(A{\displaystyle \cap B}\right)=\left\{5,6,7\right\}{\displaystyle \cap \left\{1,2,3,4,6\right\}}=\left\{6\right\}$
$C{\displaystyle \cap D=\left\{8,9,10\right\}}{\displaystyle \cap \left\{1,7,9\right\}}=\left\{9\right\}$
Than, union these two sets.
$\left(A{\displaystyle \cap B}\right){\displaystyle \cup \left(C{\displaystyle \cap D}\right)}=\left\{6\right\}{\displaystyle \cup \left\{9\right\}}=\left\{6,9\right\}$