3 sets Venn Diagram questions

Hey Louis14, All the best with your final preparations.

For this you basically need to understand why you subtract twice in one formula and why add in the other.

A - Exactly one group members in A + Exactly 2 Group Members in AB and AC + Exactly 3 group members in ABC
B - Exactly one group members in B + Exactly 2 Group Members in AB and BC + Exactly 3 group members in ABC
C - Exactly one group members in C + Exactly 2 Group Members in AC and BC + Exactly 3 group members in ABC

Thus when you add A+B+C = Exactly one group members individually in A, B and C + 2 (2 group members of AB, BC and AC) + 3 (3 group members of ABC)

Finally you want Total = Exactly one group members of A, B and C + Exactly 2 group members of AB, BC and AC + Exactly 3 group members of ABC

Thus as you can see when you add A+B+C you have added an extra (Exactly 2 group members of AB, BC and AC) and have added 2 extras of (Exactly 3 group members of ABC) - This is to say when those AB, BC and AC sets given to you do not include 3 group members.

Thus you subtract the extras to get the final total.

Formula 2 is valid when AB, BC and AC sets include those 3 group members of ABC. If that is the case :-
2 group members of AB and AC; 2 group members of AB and BC; 2 group members of AC and BC will include 3 group members in them as well. Thus when you are subtracting once from A+B+C, you are essentially subtracting 3 the (3 group members). But you need one time the 3 group members of ABC to count them in the total. Hence you add once the 3 group members.

I don't how clear was the above explanation, but I hope it does give a lil better understanding.