Question

I need help with unions, intersections, and complements involving 2 sets

Answer 1

$\begin{gathered} A)\mleft\lbrace1,2,4,7\mright\rbrace \\ B)\mleft\lbrace2,4,8\mright\rbrace \end{gathered}$

Here, we want to get the set resulting from the given set operations

a) This set is the complement of the intersection of the subsets C and D

The intersection refers to that set that has its members as the elements present in both subsets

The intersection here is;

$\mleft\lbrace8\mright\rbrace$

Now, the complement here are the other elemnts present in the universal set

We have this as;

$\mleft\lbrace1,2,4,7\mright\rbrace$

b) Here, we want to get a union

The complement of set C are the elements that not present in set C but are in the universal set

So, the union here is are the list of elements in both set, without no repetitions

$\begin{gathered} C^{\prime}\text{ = }\mleft\lbrace2,4\mright\rbrace \\ D\text{ = }\mleft\lbrace2,8\mright\rbrace \\ C^{\prime}\text{ U D = }\mleft\lbrace2,4,8\mright\rbrace \end{gathered}$