Chapter 2.2, Problem 15E

Let $A=\left\{1,2,4,5,6,9\right\},B=\left\{1,2,3,4\right\}$, and $C=\left\{5,6,7,8\right\}$.

(a) Draw a Venn diagram showing the relationship between these sets. Show which elements are in which region.

(b) What are the elements in each of the following sets?

i. $\left(A\cup B\right)\cap C$

ii. $A\backslash \left(B\backslash A\right)$

iii. $\left(A\cup B\right)\backslash \left(A\cap C\right)$

iv. $A\oplus C$

v. $\left(A\cap C\right)\times \left(A\cap B\right)$