Answer
a) $$A\cup B=\{1,3,5,6,7,9\}$$
b) $$A\cap B=\{3,9\}$$
c) $$A\cup C=\{1,2,3,4,5,6,7,8,9\}$$
d) $$A\cap C=\{\}=\varnothing$$
e) $$A-B=\{1,5,7\}$$
f) $$B-A=\{6\}$$
g) $$B\cup C=\{2,3,4,6,8,9\}$$
h) $$B\cap C=\{6\}$$
Work Step by Step
$A=\{1, 3,5,7,9\}$, $B=\{3,6,9\}$, $C=\{2,4,6,8\}$
*Things to remember on operations of sets: $$X\cup Y=\{x|x\in X \lor x\in Y\}$$ (a set comprising of all elements appearing in set $X$ or set $Y$)
$$X\cap Y=\{x|x\in X \land x\in Y\}$$ (a set comprising of only elements that appear both in set $X$ and set $Y$)
$$X - Y=\{x|x\in X\land x\notin Y\}$$ (a set comprising of only elements that appear in set $X$ but not in set $Y$)
a) $A\cup B$
Set $A$ has elements $1,3,5,7,9$ and set $B$ has elements $3,6,9$. Overall, 2 sets have elements $1,3,5,6,7,9$, which means $$A\cup B=\{1,3,5,6,7,9\}$$
b) $A\cap B$
Both sets have only 2 common elements, which are $3$ and $9$. Therefore, $$A\cap B=\{3,9\}$$
c) $A\cup C$
Set $A$ has elements $1,3,5,7,9$ and set $C$ has elements $2,4,6,8$. Overall, 2 sets have elements $1,2,3,4,5,6,7,8,9$, which means $$A\cup C=\{1,2,3,4,5,6,7,8,9\}$$
d) $A\cap C$
Both sets do not have any common elements. Therefore, $$A\cap C=\{\}=\varnothing$$
e) $A-B$
Set $A$ has elements $1,3,5,7,9$, but 2 elements $3$ and $9$ are also in set $B$. Therefore, these 2 elements are not included in set $A-B$. So, $$A-B=\{1,5,7\}$$
f) $B-A$
Set $B$ has elements $3,6,9$, but 2 elements $3$ and $9$ are also in set $A$. Therefore, these 2 elements are not included in set $B-A$. So, $$B-A=\{6\}$$
g) $B\cup C$
Set $B$ has elements $3,6,9$ and set $C$ has elements $2,4,6,8$. Overall, 2 sets have elements $2,3,4,6,8,9$, which means $$B\cup C=\{2,3,4,6,8,9\}$$
h) $B\cap C$
Both sets have 1 common element, which is $6$. Therefore, $$B\cap C=\{6\}$$
