XZAME

Math Pointer #3

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

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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