Basic Set Formulas

Here are the essential formulas derived from set theory.

Let's consider two sets A and B,

1. n(A U B) denotes the quantity of elements found in either set A or B.
2. n(A ⋂ B) denotes the quantity of elements found in both sets A & B.
3. n(A U B) = n(A) + (n(B) – n (A ⋂ B)

For three sets A, B, and C,

Illustrative Examples of Set Formulas

Example 1: In a school, there are 120 students, 40 are interested in football and 50 are interested in basketball. 15 are interested in both. How many students are interested in either of the sports or not interested at all?

Solution:

Number of football interested students, n(f) = 40

Number of basketball interested students, n(b) = 50

Number of students who like both, n(f∩b) = 15

Number of students who like either of them,

n(fᴜb) = n(f) + n(b) – n(f∩b)

→ 50+40-15 = 75

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