Notes on Types of Set and Set Relation | Grade 7 > Compulsory Maths > Sets | KULLABS.COM

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#### Types of Sets

Depending on the number of elements contained by the sets, they are classified into the following types:

• Empty or Null set
• Unit or Singleton set
• Finite and Infinite set
A set which does not contain any elements is called empty or null set. It is denoted by a symbolΦ called 'Phi'. For example:
A = {prime number between 8 and 10}
Since there is no prime number between 8 and 10. So, set A =Φ

2. Unit or Singleton Set:
A set containing only one element is called a unit set or singleton set. For example:
N = {whole number less than 1}
Since the whole number, less than 1 is 0 which is a single term. i.e N = {0}. So, the set N is said to be a unit or singleton set.

3. Finite and Infinite Set:
A set which contains a finite number of elements is called a finite set. For example:
A = {odd number between 5 and 15}
Here, A = {7, 9, 11, 13}
Since we can express the given set in cardinal number i.e. n(A) = 4, It is said to be a finite set.
A set containing never-ending elements (i.e. infinite number of elements) is called an infinite set. For example:
P = {x : x is a set of prime numbers} i.e. P = {1, 2, 3, 5, 7, 11, 13,.....................}.
The given set P is so large that we cannot express it in cardinal form. It has an infinite number of elements. So, it is an infinite set.
(Note: Infinite sets cannot be expressed in roster form)

#### Set Relations

Depending on the types of elements containing by two or more than two sets, the relationship between them can be presented in the following ways:

• Equal sets
• Equivalent sets
• Overlapping sets
• Disjoint sets
1. Equal Sets:
Two sets are equal to be equal if both the sets have exactly the same elements. The equals set is denoted by the symbol '='. For examples:
A = {a, b, c, d, e}
B = {e, d, c, b, a}
Here, n(A) = 4 and n(B) = 4. Hence sets A and B are said to be equal set and expressed as A = B.

2. Equivalent Sets:
Two sets are said to be equivalent sets if they contain the same number of elements. It is denoted by the symbol '↔' or '∼'. For examples:
A = {1, 2, 3, 4 ,5}
B = {p, q, r, s, t}
Here, n(A) = 5 and n(B) = 5. Since they have the same cardinal number so they are said to be equivalent set and is expressed as A∼ B.

3. Overlapping Sets:
Two or more than two sets are said to be overlapping sets if they consist at least one common element. For examples:
A = {2, 4, 6, 8, 10, 12}
B = {3, 6, 9, 12, 15}
In both sets A and B, 6 and 12 are common, so sets A and B are overlapping sets.

4. Disjoint Sets:
Two or more than two sets are said to be disjoint if they do not have any of the elements common. For example:
A = {1, 2, 3, 5, 7, 11}
B = {4, 12, 16, 20}
In both sets, A and B none of the elements are common so set, A and B are disjoint.

• Empty set is denoted by a symbolΦ called 'Phi'.
• The equals set is denoted by the symbol '='.
• It is denoted by the symbol '↔' or '∼'.
.

### Very Short Questions

Solution :

Here , P = { a,e,i,o,u} and Q={a,b,c,d,e}

a) Now , P ∪ Q = { a,b,c,d,e,i,o,u }

The shaded region represents the elements of P ∪ Q.

b) P ∩ Q = { a,e}

The shaded region represents the elements of P ∩ Q.

c) P - Q = { i,o,u}

The sheded region represents the elements of P - Q .

d) Q - P={b,c,d}

The shaded region represents the elements of Q -P .

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2 types
4 types
5 types
3 types
• ### A set which does not contain any elements is called _______.

finite set
infinite set
empty or null set
unit or singleton set

ø
Θ
Φ
φ

infinite set
null set
finite set
unit set
• ### A set which contains a finite number of elements is called ______.

singleton set
empty set
finite set
infinite set

null set
finite set
infinite set
unit set

=

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