First, do both of the parentheses. Do the intersection of sets A and C, which means to include elements in common to both.

Then do the union of sets B and D, which means to include all the elements in both sets without including duplicates.

Finally, do the intersection of your answers from the two parentheses including the elements common to both.

Step 1: Recall what is the definition of the intersection of two sets.

The intersection of any two sets is defined as another set that contains only the shared elements between the two sets.

Step 2: Find the elements that are shared...

The elements that are shared are: .

Step 3: Write the answer in the correct form:

 means the union of set B and set C. Union means to include all the numbers that are in either set B or set C (without listing duplicates twice). The numbers 1, 3, 5, 8, 9, and 11 appear in B and the numbers 2, 3, 5, 6, 9, 12 appear in C. Including all of those numbers in the set symbol gives the correct answer.

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