Set Theory

The study of sets helps in increasing the degree of relations in such a way that it optimizes the bond

between any two ,three or many quantities taken together.

What is a Set?

Set: A well-defined collection of objects is defined as a set.

Example: Set of vowels A= {a, e, i, o, u}

Note: All the sets are denoted by capital letters

Symbols used in sets:

Union: U

Intersection: ∩

Subset: C

Common Data Set

If there are two sets given say A and B then the common data found in these two sets is called common data set.

Example A= {a, e, i, o, u} B= {a, i, o}

Then we find the common data set between these two sets namely A ∩ B = {a, i, o}.

Union of Sets

The joining of two set elements together is called union of sets

Example: A= {2, 5, 7} B= {a, g, h}

AUB = {a, g, h, 2, 5, 7}

Intersection of Sets

Example A= {1, 5} B= {5}

Then we find the common data set between these two sets namely A ∩ B = {5}.


Cardinal Number

What is a cardinal number? The number of elements in the given set is called a cardinal number.

Example: A= {1, 2, a, v}

In the above example there are 4 elements in the given set.

Hence we define cardinal number as 4.

Sets Solved Problems

Given A= {1, 2} B= {6, 3}


1. A ∩ B

2. AUB

3. Cardinal number of A and B

If A= {2, 6, 7, 8} B= {2, 6, 3} find A ∩ B

Set Intersection

A ∩ B = {2, 6}, so the common elements are shaded in yellow.

In a total of 30 players , 25 play hockey and 10 play Rugby can you predict using set theory that how players are liking to play both.

The formulae is n (A U B) = n (A) + n (B) - n (A ∩ B)

Here n (A U B) = cardinal number of both set A and set B (hockey and rugby)

n (A)= cardinal number of only set A (Hockey only)

n (B) = cardinal number of only set B (Rugby).


n (A ∩ B) = cardinal number for both hockey and rugby

30 = 25 +10 - n (A ∩ B) so transfer n (A ∩ B) towards left side we get

n (A ∩ B) = 35-30

= 5

So the number of players who play both is 5.

Next Chapters

Number Theory Linear Equation Set Theory Math Fractions
Math Functions Pyramid Calculus Cone
Cylinder Chain Rule Limits and Continuity Prime Factorization
Square Roots and Cube Roots Parabola Distance Formula Definite Integrals
Interest Simple Interest Compound Interest Area of Irregular Figures

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