Hi
chetan2uThanks very much for the explanation. Appreciate it.
i'd like to follow up with another question here.
Now i get the difference between the two:
(sum of 2−group overlaps) = (sum of exactly 2) + 3f. correct?
My question is:
when I'm provided with individual values of d, e, f, and g. why do I get an incorrect answer when i use the second formula?
For example:
Example 1: Workers are grouped by their areas of expertise, and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers are on both the Sales and Vision teams, 9 workers are on both the Marketing and Vision teams, and 4 workers are on all three teams. How many workers are there in total?
The answer here is 74 and not 62.
1st equation: 20 + 30 + 40 - ..................
wait, i think i got it.
When we are given the value for d e and g we must subtract the value of f from each of these values for them to be valid in the second equation.
1st equation: 30 + 40 + 20 - (5+9+6) + 4 = 74
2nd equation: 30 + 40+ 20 - (1+5+2) - 2(4) = 74
Thanks a lot
chetan2u 
P.S. If you were in Calcutta, i'd buy you pizza :p