A Question on Set Theory

• Jan 22nd 2008, 07:51 PM
Norman Smith
A Question on Set Theory
Hello everyone! I hope you are all doing well today, and I am sorry I haven't been here in a while, but I guess that also shows that I may have a better time handling these questions in Precalculus now (Whew).

Anyway, I wanted to ask a question regarding the Set Theory which states:

At a picnic 12 people ate hamburgers, 20 ate frankfurters and 18 had ribs. Everyone had something to eat. Suppose 3 people ate both hamburgers and frankfurters, 6 people ate both frankfurters and ribs, 4 people had hamburgers and ribs, and 1 person ate all these types of food. How many people went on the picnic?

Thank you for all the help, and I hope that all of you are doing well.

-Norman
• Jan 22nd 2008, 11:01 PM
CaptainBlack
Quote:

Originally Posted by Norman Smith
Hello everyone! I hope you are all doing well today, and I am sorry I haven't been here in a while, but I guess that also shows that I may have a better time handling these questions in Precalculus now (Whew).

Anyway, I wanted to ask a question regarding the Set Theory which states:

At a picnic 12 people ate hamburgers, 20 ate frankfurters and 18 had ribs. Everyone had something to eat. Suppose 3 people ate both hamburgers and frankfurters, 6 people ate both frankfurters and ribs, 4 people had hamburgers and ribs, and 1 person ate all these types of food. How many people went on the picnic?

Thank you for all the help, and I hope that all of you are doing well.

-Norman

Add up the numbers for each type of food: 12+20+18=50

Now we have counted those that ate exactly 2 food types twice

So remove the numbers that ate 2 food types the number is 50-(3-6-4)=37

Now at the first stage we counted the guy who ate three food type 3 times, then at the second stage we removed hime three times so now we need to add him back in to get 38 people attended.

(look up inclusion-exclusion principle)

RonL