Please help with these 2 math problems involving sets!

[bonbons94]

These are supposed to be done using sets (and optionally venn diagrams) but I'm so confused. I have no idea how to do them!

1) 81 cities were surveyed to determine sports teams. 19 had soccer, 21 had football, 17 had basketball, 9 had soccer and football, 8 had soccer and basketball, 12 had football and basketball, and 4 had all 3.

a) How many had exactly 2 teams?

b) How many had soccer and football, but not basketball?


2. A survey of 100 inhabitants was taken to see which restaurants are liked in Pittsburg, and the following results are found. 62 like Betty's, 47 like Stella's, 32 like Larry's, 17 like Larry's and Betty's, 20 like Betty's and Stella's, 12 like Stella's and Larry's, and 5 like all three. How many like none of the 3 restaurants?

I appreciate any help given, I'm desperate! Thanks so much. =)

 

[Deleted member 4993]

These are supposed to be done using sets (and optionally venn diagrams) but I'm so confused. I have no idea how to do them!

1) 81 cities were surveyed to determine sports teams. 19 had soccer, 21 had football, 17 had basketball, 9 had soccer and football, 8 had soccer and basketball, 12 had football and basketball, and 4 had all 3.

a) How many had exactly 2 teams?

b) How many had soccer and football, but not basketball?


2. A survey of 100 inhabitants was taken to see which restaurants are liked in Pittsburg, and the following results are found. 62 like Betty's, 47 like Stella's, 32 like Larry's, 17 like Larry's and Betty's, 20 like Betty's and Stella's, 12 like Stella's and Larry's, and 5 like all three. How many like none of the 3 restaurants?

I appreciate any help given, I'm desperate! Thanks so much. =)

Draw Venn diagrams and tell us what you found.

Please show your work to us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[SB28210]

this is much easier to work with venn diagrams but I don't know how to draw them on this program bon:

P(soccer) = 19
P(Football) = 21
P(Basketball) = 17

P (Soccer intersect Football) = 9 this set includes 5 soccer and foot ball only and 4 Soccer and Football and Basketball
p (Soccer intersect Basketball) = 8 this set includes 4 soccer and basketball only and 4 Soccer and Football and Basketball
P (Football intersect Basketball) = 12 this set includes 8 basketball and foot ball only and 4 Soccer and Football and Basketball

P (Soccer intersect Football interset Basketball) = 4

We're asked for how many cities have just two teams so it should be asy to figure out now...

The second problem:

First find out all the people who like all the restaurants and subtract that from 100:

P(A U B U C) = P(A) + P(B) + P(C) - [P(A and B) + P(A and C) + P(B and C)] - P(A and B and C)

100 - {(P(Bettys) + P(stellas) + P(Larrys)) - (P(Larry and Betty) + P(Betty and Stella) + P(Stella and Larry)) - P(Betty and Stella and Larry)}

the problem gives you all this information so all you need to do is just plug it in.

hope this helps