# Set Operations

• Jan 25th 2009, 10:09 PM
ruckerbo
Set Operations
I am not understanding these concepts at all, and I have to solve these two word problems.

"A survey of 500 television watches produces the following results: 285 watch football games, 195 watch hockey games, 115 watch basketball games, 45 watch football and basketball games, 70 watch football and hockey games, 50 watch hockey and basketball games, and 50 don't watch any of the three types of games.

a. How many people watch all three types of games?

b. How many people watch just one type of sport?"

And this one too.

"Of 100 people questioned, 37 eat fruits, 33 eat vegetables, 9 eat cheese and fruits, 12 eat cheese and vegetables, 10 eat fruits and vegetables, 12 eat only cheese, and 3 eat all three offerings.

a. How many people surveyed eat cheese?

b. How many do not eat any of the offerings?"
• Jan 27th 2009, 03:54 AM
Venn diagram
Hello ruckerbo
Quote:

Originally Posted by ruckerbo
I am not understanding these concepts at all, and I have to solve these two word problems.

"A survey of 500 television watches produces the following results: 285 watch football games, 195 watch hockey games, 115 watch basketball games, 45 watch football and basketball games, 70 watch football and hockey games, 50 watch hockey and basketball games, and 50 don't watch any of the three types of games.

a. How many people watch all three types of games?

b. How many people watch just one type of sport?"

And this one too.

"Of 100 people questioned, 37 eat fruits, 33 eat vegetables, 9 eat cheese and fruits, 12 eat cheese and vegetables, 10 eat fruits and vegetables, 12 eat only cheese, and 3 eat all three offerings.

a. How many people surveyed eat cheese?

b. How many do not eat any of the offerings?"

For question 1, draw a Venn diagram like the one I've attached. F is the set of all people who watch football, H those who watch hockey and B those who watch baseball.

Start in the centre. These are the people who watch all three. Call this number x, and work out from the centre, filling in the numbers in each region. Remember that the numbers in the question are the totals in each case. So, for example, there are 45 altogether who watch football and baseball. And we have located x of them: they're the ones who watch all three, and they are in the centre of the diagram. So there are (45 - x) left who watch football and baseball, but not hockey.

I've filled in all four sections in set F. Check that you can see where I get those from. Then fill in the remaining sections of sets B and H in a similar way.

Then enter the number 50 outside the three loops - they are the people who don't watch any of these sports.

Finally, add up the numbers and x's in all eight of the regions, and put the answer equal to 500, because that is the total number of people surveyed.

Solve this equation for x, and you're done for part a. Don't forget to answer part b as well.

For question 2, draw a similar diagram. Start in the centre again, only this time you don't need x: you can fill the number in immediately. Work outwards as before, filling in all the numbers that you can. This time, you know the total is 100 so you can work out any missing numbers from that.

Can you complete these questions now?