A collection of objects is called a Set.

## Formulas of Sets

These are the basic set of formulas from the set theory.

If there are two sets P and Q,

- n(P U Q) represents the number of elements present in one of the sets P or Q.
- n(P ⋂ Q) represents the number of elements present in both the sets P & Q.
- n(P U Q) = n(P) + (n(Q) – n (P ⋂ Q)

For three sets P, Q, and R,

- \(n(P U Q U R) = n(P) + n(Q) + n(R) – n(P\bigcap Q) – n(Q\bigcap R) – n(R\bigcap P) + n(P\bigcap Q\bigcap R)\)

## Examples of Sets Formulas

**Example 1: ** In a class, there are 100 students, 35 like drawing and 45 like music. 10 like both. Find out how many of them like either of them or neither of them?

Solution:

Total number of students, n(\(\mu\)) = 100

Number of drawing students, n(d) = 35

Number of music students, n(m) = 45

Number of students who like both, n(d∩m) = 10

Number of students who like either of them,

n(dᴜm) = n(d) + n(m) – n(d∩m)

→ 45+35-10 = 70

Number of students who like neither = n(\(\mu\)) – n(dᴜm) = 100 – 70 = 30

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