So this is big. I have been struggling with Venn diagram related problems. Not that I am dumb or mathematically illiterate but it’s just taking too much of time when I try to solve them. So here is my new raw deal. I am not getting into the whole concepets of P(aUbUc) = P(A) … thing. It’s just gets on my nerves. My simplistic formula is this:

Venn diagram

- T = Grand Total (All the students)
- E = Extra (e.g: number of students who do not study any of the subjects)
- A = 1st inclusive set (Students registered for English)
- B = 2st inclusive set (Students registered for Math)
- C = 3st inclusive set (Students registered for Zoology)
- M = Set including both 1st and 2nd (Students registered for both English and Math)
- N= Set including both 1st and 2nd (Students registered for both Math and Zoology)
- P = Set including both 1st and 2nd (Students registered for both Zoology and English)
- O = All inclusive (Students registered for English, Math and Zoology)
- X = Only 1st set (Students registered only for English)
- Y= Only 1st set (Students registered only for Math)
- Z= Only 1st set (Students registered only for Zoology)

Formula: T – E = A + B + C – 2 ( O ) – [ M + N + P ], Sometimes E will be zero in some problems.

Also, sub formulae:

- T – E = X + Y + Z + M + N + P + O
- A = X + M + N + O
- B= Y + N + P + O
- C = Z + P + M + O
- A + B + C = X + Y + Z + 2 [ M + N + P ] + 3 ( O ).
- Therefore,
- A + B + C = X + Y + Z + [ M + N + P ] + ( O ) + [ M + N + P ] + 2 (0)
- A + B + C = T – E + [ M + N + P ] + 2 (0)

Just remember the formula and not the sub-formulae. Pick any set related question and I assure you that it will be a breeze ;). Try this question for kicks: Set Question .

Ciao Myte!

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