Question

writ the formula for complete of sets.


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Answer 1

Step-by-step explanation:

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(PUQUR)=n(P)+n(Q)+n(R)–n(P⋂Q)–n(Q⋂R)–n(R⋂P)+n(P⋂Q⋂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(μ) = 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(μ) – n(dᴜm) = 100 – 70 = 30