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**Lauren1415****Member**- Registered: 2018-10-17
- Posts: 14

1. Problem Solver: A cat has thirteen kittens. Eight of the kittens have white hair, six of the kittens have spots, and eight of the kittens have long tails. All of the kittens have at least one of these traits. One kitten is white with spots and a long tail. Three of the kittens are white with spots. Two kittens have spots and long tails. One kitten has white hair but does not have spots or a long tail.

a. Draw a Venn diagram for this problem. (You can upload a hand-drawn picture or type out the values in all 7 sections of the diagram.)

b. How many kittens are white with long tails, but don't have spots?

My answer:

6 Kittens are white with long tails, but don't have spots.

13 total

white: 8-1

spot: 6

long tails: 8

white with spots: 3

long tails with spots: 2

white with long tails: 6

white with spots and a long tail: 1

my teacher said,

#1 -" Your diagram values are incorrect. Let's start with 1 in the very middle (which you have). Then, you have "Three of the kittens are white with spots." You just recorded that one kitten is white with spots and a long tail. How many kittens does that leave that are white with spots but not a long tail? That value goes in the section for while with spots only."

I don't understand, please help.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,826

Hi Lauren1415,

Please see this link in MathsIsFun.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,452

hi Lauren1415

Venn problems with three sets involved look like this:

So **A** might be kittens with white hair and **B** might be white spots, for example.

There are eight regions altogether : such as **s** = kittens with white hair but no spots and no long tail, and **w** = kittens with all three characteristics.

So start by drawing three overlapping circles and label on the outside "white hair" etc.

Then you have to read the information carefully so that the correct numbers go in each region. We're told that all kittens have at least one trait so **z** = zero.

And "One kitten has white hair but does not have spots or a long tail" so we can put in **s** = 1.

Some regions cannot be entered without some calculation eg. "Three of the kittens are white with spots" means they must be in **A** and also in **B**. But we don't yet know how to decide how much is **t** and how much **w**. But we do know that **t + w** = 3. Don't enter that as it's not the number for a single region.

But there's enough information to work out t and w separately, and once you have, you can enter the correct numbers. Keep doing this with all the information and you'll find that all eight numbers can be determined.

Check you've done it right by adding up numbers in regions to check it tallies with the information. All eight numbers should add up to 13 for example.

Try this and if you're still stuck post back what you think s, t, u etc are and I'll have a closer look for you.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,609

Hi Ganesh and Bob;

Can you solve this one? I can't.

I looked up Ganesh's MIF link to learn about Venn, but maybe I didn't understand it all and am reasoning it wrong.

A couple of questions about Bob's post first, though, before I try again:

There are eight regions altogether : such as

u= kittens with white hair but no spots and no long tail

cf.

And "One kitten has white hair but does not have spots or a long tail" so we can put in

s= 1.

Shouldn't **u** be **s**?

But we do know that

t + w= 3.

Hmm...is that right? I get something else.

Thanks!

*Last edited by phrontister (2019-01-20 09:52:14)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,452

hi phro,

Yes that first u should have been s. I refer the reader to my signature statement.

I have drawn the diagram and entered eight numbers into the regions. I still think t + w = 3. My sequence of solving is:

z, w, then t, then v, then x, then u, then y. Adding, these total to 13 as required so I'm unsure why you think there's a problem with the question.

When it says "Three of the kittens are white with spots." I interpret this as meaning the union of white and spots. I didn't assume I was being told anything about those three kittens' tails. Hence t + w.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,609

Thanks, Bob...I've now solved it.

When it says "Three of the kittens are white with spots." I interpret this as meaning the union of white and spots. I didn't assume I was being told anything about those three kittens' tails. Hence t + w.

That's where I went wrong: I'd misinterpreted that, and didn't apply the union. And so t + w = 3 is right.

z, w, then t, then v, then x, then u, then y.

You're testing me again!

Btw, I solved them in this order: w, t, x, s, v, y, u.

There would be other orders, too.

*Last edited by phrontister (2019-01-22 10:07:20)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**Lauren1415****Member**- Registered: 2018-10-17
- Posts: 14

thank you, I figured it out!

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