When you see a letter with the prime symbol, that means complement. Complement tells you to take whatever is NOT in that set and what is in the universal set. You could also say you are eliminating the numbers in the universal set that are in the set you are complementing.

The universal set is

Set

Taking the numbers 7, 8, 9, and 10 out of the universal set you get the answer

The prime symbol means to take the complement of set D. To find a complement, you want to only include the numbers in the universal set that do not appear in the set being complemented.

If set  

and the universal set is 

The numbers you want to include are everything in the universal set except 4, 9, 10, 11, and 12

This leaves the numbers

A complement symbol means you want to only include the numbers in the universal set that do not appear in the set being complemented.

However, all the numbers in the universal set appear in itself. This means the complement of ANY universal set is the empty set.

Always work in parentheses first. First, you need to solve the union of sets A and B. Union means to include everything in both sets without repeating any duplicates.

Now take the complement of this by including the numbers in the universal set that do not appear in A union B. This leaves

Step 1: Recall the definition of Complementary angles. 

Two angles are complementary if the sum of the two angles is ALWAYS .

Step 2: If the sum of the angles is , then we can subtract the other one to find the missing angle...

So, 

The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it

Flip the intersection symbol to a union, complement both sets, and add parentheses with the complement symbol outside of it.

The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.

Flip the symbol from an intersection to a union, complement both sets, and remove the parentheses.

 is equivalent to the original statement

The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.

Flip the union symbol to an intersection, complement both sets, add parentheses and a complement symbol outside the parentheses.

The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.

Flip the union symbol to an intersection symbol, complement both sets, and remove the parentheses

The first step is to realize that the C and intersection symbol in the original question are distractions and have nothing to do with applying DeMorgan's Law.

In the parentheses, flip the symbol from an intersection to a union and complement both sets.

Normally, with only two sets, you should eliminate the parentheses that was there to show that the complement symbol applied to the entire parentheses. However, with three sets you still need to know the order in which to work out the problem so you should keep the parentheses around B and A.