A collection of objects is called a Set.

## Formulas of Sets

These are the basic set of formulas from theÂ 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(PÂ â‹‚Â Q) represents the number of elements present in both the sets P & Q.
- n(P U Q) = n(P) + (n(Q) â€“ n (PÂ â‹‚Â Q)

For three sets P, Q, and R,

- \(n(P U Q U R) = n(P) + n(Q) + n(R) â€“ n(P\bigcap Q) â€“ n(Q\bigcap R) â€“ n(R\bigcap P) + n(P\bigcap Q\bigcap R)\)

## Examples of Sets Formulas

**Example 1:Â **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(dâˆ©m) = 10

Number of students who like either of them,

n(dá´œm) = n(d) + n(m) â€“ n(dâˆ©m)

â†’ 45+35-10 = 70

Number of students who like neither = n(\(\mu\)) â€“ n(dá´œm) = 100 â€“ 70 = 30