Mishari wrote:

Here is the theoritical equation:

T = G1 + G2 + G3 - G1G2 - G2G3 - G1G3 - 2B

where:

GxGy: both Gx and Gy (overlapping)

B: All G1, G2, and G3 (overlapping)

T: total

Derivation:

Total = G1only + G2only + G3only + G1G2 + G2G3 +G3G1 + B (covering all possible groups)

example: total students = only milk + only chicken + only apples + both milk and apple + both apple and chicken + both chicken and milk + all milk,chicken, and apple

G1only = G1 - G1G2 - G1G3 - B

G2only = G2 - G1G2 - G2G3 - B

G3only = G3 - G1G3 - G2G3 - B

plug in equations in the main equation above:

Total = G1 - G1G2 - G1G3 - B + G2 - G1G2 - G2G3 - B + G3 - G1G3 - G2G3 - B + G1G2 + G2G3 + G1G3 + B

Total = G1 + G2 + G3 - (G1G2 + G1G3 + G2G3) - 2B

Great explanation, THX!!!

But, If you're not so algebraic, like me =) You can also see this conceptually why this is true. Because just by looking at the derived equation, one might wonder, why? Or for me, why "-2B?" Why not just -B?

I enlightened myself by making an actual Vann diagram. With 3 post-its, I made three circles and overlapped them. Then it became so clear why the equation tells you to do -2B instead of -B or -3B

anyone like me, who just can't ACCEPT the equation as is, unless you actually SEE it, it might help.