Advanced Math/SET THEORY

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Expert: - 7/28/2010


Question
In a group of 50 students,there are 30 males and 40 vegetarians and
25 male vegetarians .find the number of
a) Female vegetarians
b) Male and female  non-vegetarians .

Answer
a) If there are 50 students and 30 males,
  this means the number of females is N where N = 50 - 30.

b) Since all people are either male or female, that looks like all of the non-vegetarians.
  Since there are 50 people with 40 vegetarians, that would make M non-vegearians,
  where M = 50 - 40.


For a more thorough explanation, ...

What this problem says is that there are 30 males and 40 vegetarians.
This means that there are 50-30=20 females and 50-40=10 non-vegetrians.
It says there are 25 male vegetarians, so there are 30-25=5 meat eating males.
If 25 of the vegetarians are male, 40-25=15 are female.
Sine there are 20 females and 15 of them are vegetarians, 20-15=5 of them eat meat.

So with M for male, F for female, V for vegetarians, and X for meat eaters, we have
25 MV, 5 MX, 15FV, and 5 FX.  That is a total of 50 people.

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