In a survey on the soda preferences of football players, it was found that

22 like grape soda. 25 like Sprite. 39 like Coke.

9 like Sprite and grape soda. 17 like grape soda and Coke. 20 like Sprite and Coke.

6 like all flavors. 14 like none.

A set of players who like grape soda; B set of players who like Sprite; C those who like Coke.

a) [6 pts] How many players were surveyed? ____ . (Not just give an answer, show how you got it).

b) [24pts=3pts for each subproblem for 8 areas;]

Figure out values of areas (subsets) #1 - #8.

Important: values dont go out of borders. For example, there are 22 people who like grape soda, but you cannot put number 22 anywhere into set A, as A consists of 4 subsets (see Venn diagram below).

You must provide explanations on how you got each of those numbers to receive full credit (1 pt for correct values + 2pts for explanations for each of 8 subproblems). Hint on how to explain - give set expression of the area of interest as formula, show how to derive its cardinality.

1. Value for #1: ____________

Explanations:

2. Value for #2: ____________

Explanations:

3. Value for #3: ____________

Explanations:

4. Value for #4: ____________

Explanations:

5. Value for #5: ____________

Explanations:

6. Value for #6: ____________

Explanations:

7. Value for #7: ____________

Explanations:

8. Value for #8: ____________

Explanations:

explanations on hoW you got each or those hufmbers to receive iuil credit. How to type: I provide you here with 8 #2 #5 #6 #1 #3 #4 #7 #8