Math Is Fun Forum

mantastrike

Member

Registered: 2011-04-24

Posts: 64

N(A ∪ B ∪ C) = Using Inclusion/Exclusion of 3 sets please help me!!

A study has been done to determine if three different drugs - A, B and C - help relieve headache paint. 60 subjects were given the drug and the following results records.

18 reported drug A worked.
24 reported drub B worked.
33 reported drug C worked.
7 reported both drug A and B worked.
15 reported both drug A and C worked.
21 reported both B and C worked.
36 reported that at least one of the drugs worked.

i. How many people felt none of the drugs worked?
ii. How many people found all three drugs worked?
iii. How many people found only Drug B worked?
iv. Draw a Venn diagram to represent the data.
v.State two more pieces of information you can now read from the Venn diagram.

It's like this:
A, B, and C are any finite sets, then

N(A ∪ B ∪ C) = N(A) + N(B) - N(C) - N(A ∩ B) - N(A ∩ C) - N(B ∩ C) + N(A ∩ B ∩ C)

PLEASE HELP ME!! I would really like a venn diagram for this as well.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: N(A ∪ B ∪ C) = Using Inclusion/Exclusion of 3 sets please help me!!

Hi;

Hasn't this question been answered for you over here?

http://www.mathisfunforum.com/viewtopic … 74#p173374

Also there is an error in your principle of inclusion exclusion formula.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: N(A ∪ B ∪ C) = Using Inclusion/Exclusion of 3 sets please help me!!

hi mantastrike

A, B, and C are any finite sets, then

N(A ∪ B ∪ C) = N(A) + N(B) + N(C) - N(A ∩ B) - N(A ∩ C) - N(B ∩ C) + N(A ∩ B ∩ C)

Are you now trying to prove this formula?

If so, use the three circle Venn diagram from the earlier post; but replace all the 'x' expressions with letters; eg:  a,b,c,d,e,f,g;  one letter per region.

Then write each bit from the formula above in terms of the letters eg N(A) = a + b + d + e etc.

Show that both sides of the equals come to the same region.

Bob

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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

mantastrike

Member

Registered: 2011-04-24

Posts: 64

Re: N(A ∪ B ∪ C) = Using Inclusion/Exclusion of 3 sets please help me!!

Hi;

Hasn't this question been answered for you over here?

http://www.mathisfunforum.com/viewtopic … 74#p173374

Also there is an error in your principle of inclusion exclusion formula.

Sorry about that mate! BTW my classmate who registered in this message board was confused because his questions were missing.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: N(A ∪ B ∪ C) = Using Inclusion/Exclusion of 3 sets please help me!!

Hi;

That was me. That was the third time within 3 days that the same question has been posted. I try to keep exact questions together. New threads for the same question just confuse everyone.

This thread for instance is in two spots. I provided a link to the answers so that they could be followed.

In the case of these questions both gAr and Bob Bundy have answered them so thoroughly that you could just copy them into your notes or your homework assignment. Which is exactly what I did, copied them to my notes.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mantastrike

Member

Registered: 2011-04-24

Posts: 64

Re: N(A ∪ B ∪ C) = Using Inclusion/Exclusion of 3 sets please help me!!

Hi;

That was me. That was the third time within 3 days that the same question has been posted. I try to keep exact questions together. New threads for the same question just confuse everyone.

This thread for instance is in two spots. I provided a link to the answers so that they could be followed.

In the case of these questions both gAr and Bob Bundy have answered them so thoroughly that you could just copy them into your notes or your homework assignment.

OK BTW, I can't figure out question iii? can u plz help me. using some formulas?