# 2. Sizes of Sets

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The following topics are included in this series of five videos.

1. Determining the size of a set in a two set Venn diagram, first example
2. Some useful formulas
3. Second example
4. Word problem example
5. Three set Venn diagram problem

Method for solving these types of problems:

1. If you have a word problem, first translate from English to math.
2. Draw a Venn diagram, and start filling it in, from the inside.
3. If you can fill in the entire diagram in this way, do so.
4. If you cannot, put a variable where you get stuck and fill in the rest of the diagram in terms of that variable. Then solve for the variable.

#### PREWORK:

1. A survey of 200 people was taken. We find 170 people like ER, 30 like Chicago Hope but not ER, and 140 like both Chicago Hope and ER. How many like neither show?
2. If $$n(U) = 24, n(R) = 8, n(S) = 12$$, and $$n(R \cup S) = 18$$, what is $$n(R \cap S)$$?

2. We look at the bottom Venn diagram. Since we don't know $$n(R\cap S)$$ we put a variable, $$x$$ in the intersection. Since there are 8 elements in $$R$$ total, there must be $$8-x$$ elements only in $$R$$. Likewise, there are $$12-x$$ elements only in $$S$$. Now $$8-x+x+12-x=18$$ since $$n(R\cup S)=18$$. We solve to get that $$x=2$$. Therefore $$n(R\cap S)=2$$.