Step 1: Recall the definition for intersection of two sets: The intersection of two sets is a subset that has numbers that is shared between two sets, A and B.

Step 2: Find the shared elements between both sets

Set A and Set B both share 4,11, and 14.

The intersection of both sets is {}

Step 1: Define the union of two sets. The union of two sets is all elements that are in two sets, as well as the elements that are shared. 

Step 2: Find the union of the sets:

Set A has elements: 
Set B has elements: 

Union of Set A and B () is {}

Step 1: Define what the intersection of two sets means.. The intersection of two sets is defined as a set that has elements that are shared between both original sets..

Step 2: Find any shared elements..

If we look, Set A and Set B do not share any elements..

Therefore, there is no intersection of the two sets.

This question asks you to find the intersection of the sets B and D. Include only the numbers that both sets have in common with one another. The only common number with both sets is 4.

Always start by doing the parentheses first. Do the union of C and B which means to include all the elements from both sets without including duplicates. The numbers do not need to be in any order. Sometimes it can help to put the elements from one entire set before putting the elements in the other

Now, take the results from C union B and do the intersection of those elements with set D. Intersection means to include the elements that are common to both sets.

The final answer is

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