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(PÂ â‹‚ Q) represents the number of elements present in both the sets P & Q.
- n(P U Q) = n(P) + (n(Q) – n (P â‹‚ Q)
For three sets P, Q, and R,
- \(\begin{array}{l}n(P U Q U R) = n(P) + n(Q) + n(R) – n(P\bigcap Q) – n(Q\bigcap R) – n(R\bigcap P) + n(P\bigcap Q\bigcap R)\end{array} \)
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(
\(\begin{array}{l}\mu\end{array} \)
) = 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(
\(\begin{array}{l}\mu\end{array} \)
) – n(dᴜm) = 100 – 70 = 30
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