Logic class
 

Quick question that's stumping me on the review material. I didn't pay much attention this day in class...now I'm paying for it xD.

2. In a class of 100 students, 35 studied French, 42 studied Spanish, 43 studied German, 17 studied French and Spanish, 15 studied Spanish and German, 13 studied French and German, and 20 did not study any of the three languages.

(a) Use a Venn-diagram and place appropriate numbers in each of the 8 regions.

(b) How many studied exactly two of three languages?

© How many studied French or German but not Spanish?

(d) How many studied Spanish only? (15points)



I figure I have to label all the areas as separate variables and add/subtract them in some series to get the variables I need, but I don't see a straightforward way to do that. Hints would be fine, just the answer is not cool if not accompanied by an explanation ^^. Looking to learn here, not have my homework done for me xD. Thanks!

Goggle image search for venn diagrams
images.google.com/images?&um=1&hl=en&safe=off&q=venn+diagram&&sa=N&start=0&ndsp=21]venn]venn diagram - Google Image Searchdiagram - Google Image Search


I like this one:
weblog.lowpro.ca/wp-content/uploads/2007/08/venn_diagram_example.gif

Don't forget wikipedias page on venn diagram

I....I'm not sure how I can help you with this short of giving you the answers. There aren't really any sub-steps you need to do to extract the information needed, just add up the appropriate groups. Do you know how to draw Venn diagrams?

Is this right? I just drew circles (Venn-diagram style) and worked on deductive reasoning based upon the givens.

I know it's been a while, but I think this is the right answer
 

You have your Venn diagram wrong.

It should look like this:
http://www.brinkleys.org/users/tsl/Files/venn.jpg

(b) How many studied exactly two of three languages? 45

© How many studied French or German but not Spanish? 33

(d) How many studied Spanish only? 10

I don't think that answer is right because when I add all the figures displayed in the venn diagram, I get 95 and not 100 students.