# Thread: finite math- venn diagrams and such.

1. ## finite math- venn diagrams and such.

the problem is as follows:

Partners in an accounting firm.

Assume that each partner has at least one specialization.

Specialization-------------Number

Auditing---------------------13
Consulting------------------14
Tax--------------------------11
Auditing and consulting-----8
Auditing and tax-------------6
Consulting and tax----------7
All three---------------------3

How many partners are there?

i know that the problem would be set up like the picture I drew below, and that i'm trying to find ((A ∪ C) ∪ T), but i just can't figure it out.

2. Originally Posted by sdsdsd
the problem is as follows:

Partners in an accounting firm.

Assume that each partner has at least one specialization.

Specialization-------------Number

Auditing---------------------13
Consulting------------------14
Tax--------------------------11
Auditing and consulting-----8
Auditing and tax-------------6
Consulting and tax----------7
All three---------------------3

How many partners are there?

i know that the problem would be set up like the picture I drew below, and that i'm trying to find ((A ∪ C) ∪ T), but i just can't figure it out.

I am not an expert on Venn diagrams as these were not discussed very well in my school years long time ago. But I find them now interesting. I just use "common sense" now in figuring them out.

I do not agree with your distribution as shown on the posted diagram.

Take the case of the partners engaged in Auditing.
Auditing ..........................13 partners
Auditing and Consulting ......8
All 3...(A +C +T) ...............3

You forgot that the 3 partners in the (A +c +T) are engaged in A and C also that is why you put 8 in the in the "compartment" for (A +C). The number there should be 5 only.

Then you put 13 on the compartment for A only. You forgot again that the 3 in the (A +C +T) and the 5 in the (A +C) are engaged in Auditing also.
And then there are partners in the (A +T) that are egaged in Auditing also...these are 3 partners.
So instead of 13, you should have put (13 -3 -5 -3) = 2 only in there.

Following the reasonings above, you should come up with 2 only (instead of 14) in the C, and 1 only (instead of 11) in the T.

In the end, the total partners are the sum of all the numbers in the diagram.
A = 2
C = 2
T = 1
A+C = 5
A+T = 3
C+T = 4
A+C+T = 3
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