Quantitative Reasoning

u = union and n = intersection

1. For 3 sets A, B, and C: P(AuBuC) : P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)

2. To determine the No of persons in exactly one set : P(A) + P(B) + P(C) – 2P(AnB) – 2P(AnC) – 2P(BnC) + 3P(AnBnC)

3. To determine the No of persons in exactly two of the sets : P(AnB) + P(AnC) + P(BnC) – 3P(AnBnC)

4. To determine the No of persons in exactly three of the sets : P(AnBnC)

5. To determine the No of persons in two or more sets : P(AnB) + P(AnC) + P(BnC) – 2P(AnBnC)

6. To determine the No of persons in at least one set : P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + 2 P(AnBnC)

(SEE THE ATTACHED PICTURE TO UNDERSTAND THE BELOW MORE CLEARLY)

1. For three sets A, B, and C, P(AuBuC): (A+B+C+X+Y+Z+O)
2. Number of people in exactly one set: ( A+B+C)
3. Number of people in exactly two of the sets: (X+Y+Z)
4. Number of people in exactly three of the sets: O
5. Number of people in two or more sets: ( X+Y+Z+O)
6. Number of people only in set A: A
7. P(A): A+X+Y+O
8. P( AnB): X+O

Hope this helps. Please add if i have missed something.