1. ## Set theory 2

a) A group of 700 tourists are visiting a city and the following information is given:

379 visited the park
419 visited the museum
260 visited the theatre
102 went to the theatre but didnt go to the park nor the museum
92 went to the museum but didnt go to the park nor the theatre
110 went to the park but didnt go to the theatre
60 went to the three places

304 tourists went to only place and 287 went to two places. Calculate how these values are obtained.

b) A car agency sold 180 units during a year with the following characteristics:

57 were standard
45 were standard and had ac
10 were standard but didnt have ac or stereo
28 were standard and had ac, but didnt have stereo
90 didnt have any of these three

22 units had stereo. Find out how this was obtained.

2. These things can be real 'head-scratchers', can't they?.

If I did this correctly, here's the Venn diagram. It's kind of lop-sided, but should put forth the idea. It would appear 22 have stereo.

3. Originally Posted by bret80
Thanks for your help, I could spend days solving these problems, so I need a bit more of your aid.

a) A group of 700 tourists are visiting a city and the following information is given:

379 visited the park
419 visited the museum
260 visited the theatre
102 went to the theatre but didnt go to the park nor the museum
92 went to the museum but didnt go to the park nor the theatre
110 went to the park but didnt go to the theatre
60 went to the three places

How many of these tourists assisted to exactly one and two of these places?
I don't really understand the question, is it how many tourists went to only one place, or two places, or three?

4. I wrote down the correct answers. I would like to know how these values are obtained. Thanks.

5. Originally Posted by bret80

a) A group of 700 tourists are visiting a city and the following information is given:

379 visited the park
419 visited the museum
260 visited the theatre
102 went to the theatre but didnt go to the park nor the museum
92 went to the museum but didnt go to the park nor the theatre
110 went to the park but didnt go to the theatre
60 went to the three places

304 tourists went to only place and 287 went to two places. Calculate how these values are obtained.

.
I got a answer that made no sense when I did it this way but got the exact answers when I assumed the 110 line should have read 110 went to the park but didn't go to the theatre nor the museum. Please could you check the question in case I did make a mistake as I am distracted by having my baby son sleep on me!

In that case 304 = 102 + 92 + 110 for only one

Exactly two is more difficult to go through here. If I'm right about the question I can send the answer as an attachment. Just tell me what format you would prefer.

6. Hi Glaysher,

Thanks for trying the figure out the answers. I assume you're right about the 110 going to neither of those places. I guess excell is fine or word.

7. See attachment. Drawing Venn diagrams in questions like this is often the best way of approaching the problem.

8. 110 went to the park but didnt go to the theatre
presumable this should have been

"110 went to the park but didnt go to the theatre nor the museum".

$x+z = 209$
$y+z = 267$
$x+z = 98$
$2(x+y+z) = 574$
hence $x+y+z = 287$