Set Formulas

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,

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

For three sets P, Q, and R,

  • [latex]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)[/latex]

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?


Total number of students, n([latex]\mu[/latex]) = 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([latex]\mu[/latex]) – n(dᴜm) = 100 – 70 = 30

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