College Math Special Problem

From the information below create a Venn Diagram labeling the circles for Pizza P, Burgers B and Nuggets N and showing cardinality of each subregion. (Don't forget some people are in the overlap of more than one). Also finish writing in the symbolic notation for the various pieces of information provided as I started to do for the first three.

20 people ate burgers total n(B)
27 people ate Pizza n(P)
21 people ate nuggets n(N)
9 people ate both burgers and nuggets
8 people ate both burgers and pizza
12 people ate both pizza and nuggets
5 people ate pizza, burgers, and nuggets this week
6 people didn't have any of these items

Answer the following:

1. How many people were surveyed?

2. How many people ate Pizza but NOT burgers

3. How many ate Nuggets or Pizza

(Note: "or" is not to say that some that you should include here did not have both, this is what is called an inclusive or. It includes those who meet both descriptions, see page 61, 93-94)

4. How many ate burgers or Nuggets but not pizza

5. In each of the previous 5 questions what was the symbolic noation for the sets you were looking for? You will need to use the letters P, B, N for the sets and then the symbols for union, intersection, and/or complement to answer.