Summary Venn Diagram

Grade 12 Mathematics Notes: Venn Diagrams
These summarized notes explain how to solve 2-set and 3-set Venn diagram problems.

1. Two-Set Venn Diagram Problems
A 2-set Venn diagram shows the relationship between two groups or sets.

 Important Terms:

 Union (A ∪ B): Elements in A or B or both.
 Intersection (A ∩ B): Elements common to both sets.
 Complement: Elements not in a set.

 Formula:

 n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

 Example:

 In a class of 40 students, 25 study Mathematics, 18 study Science, and 10 study both
subjects.
 Find how many students study at least one subject.

Solution:
n(M ∪ S) = 25 + 18 − 10 = 33
Therefore, 33 students study at least one subject.

2. Three-Set Venn Diagram Problems
A 3-set Venn diagram represents relationships among three sets.

 Formula:

 n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C)

 Steps for Solving 3-Set Problems:

 Start with the number in the middle (common to all 3 sets).
 Fill in the pair intersections next.
 Complete the individual sets.
 Add all values to check totals.

 Example:

 In a survey of 50 students:
20 like Football, 18 like Basketball, 15 like Volleyball.
5 like Football and Basketball, 4 like Football and Volleyball,
3 like Basketball and Volleyball, and 2 like all three sports.