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Expert: - 11/29/2009


Question
A and B and C are non empty sets and E is the universal set. Given that: n(AnBnC)=3, n(A)=15, n(E)=40, n(AuBuC)=32, n(A'nBnC)=6, n(AnB'nC)=8 and n(AnBnC')=4. Find: i.) n(AuB'uC), ii.) n(A-B), iii.) n[ (AuC)nB'], iv.) n(AuBuC)'.

Answer

Venn Diagram
Questioner: Edwin
Country: Poland
Category: Advanced Math
Private: No
Subject: Set theory
Question: A and B and C are non empty sets and E is the universal set. Given that: n(AnBnC)=3, n(A)=15, n(E)=40, n(AuBuC)=32, n(A'nBnC)=6, n(AnB'nC)=8 and n(AnBnC')=4. Find: i.) n(AuB'uC), ii.) n(A-B), iii.) n[ (AuC)nB'], iv.) n(AuBuC)'.
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This is a standard 'Venn Diagram' exercise.
See attached diagram, in which the various regions are numbered.  For example,

Region 1 is  A B' C'    

I use no symbol at all for intersection.  [A B means intersection of A and B.]

So:

if  n(A B C) = 3, that means n(R5) = 3.
if  n(A' B C) = 6, that means n(R6) = 6, because
A' B C means  in B, in C, not in A --- that is region 6.


Now fill in all the regions, working from the inside out.

Then you can answer all the questions.

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

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