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A set is a well-defined collection of objects.

Consider A = {x: x is a natural number and x â‰¤ 4}

A={1,2,3,4}

The number of elements in this set is four.

This is a finite number. Sets having a finite number of elements are known as non-empty finite sets.

**Non-empty Finite Set:** If the number of elements in a set S is a natural number, then S is said to be Non-empty Finite Set.

Consider a set that does not contain any element.

E = {x: x is a real solution of x^{2} + 1 = 0}

This set consists of elements that are real roots of the equation x square plus one is equal to zero.

x^{2} + 1 = 0

x^{2} = -1

**Empty Set**: A set that does not contain any element is called an Empty Set or Null Set or a Void Set.

E = {} = âˆ…

An empty set is denoted by the symbol â€” phi.

A = {1, 2, 3, 4}

E = {} = âˆ…

**Infinite Set:** A set that is empty or consists of a definite number of elements is called Finite Set, otherwise it is called an Infinite Set.

**N = {x: x is a natural number}
N = {1,2,3,4,...}
X = {a: a is solution of a**

Sets X and Y are equal since both have the same number of elements as well as the same type of elements.

**Equal Sets:** Two sets A and B are said to be equal if they have exactly the same elements and we write A=B. Otherwise, the sets are said to be unequal and we write **A â‰ B**.

**A = {1,2,3,4}** and **B = {a,b,c,d}**

Elements of these two sets are different. So, these sets are not equal to each other.

A set is a well-defined collection of objects.

Consider A = {x: x is a natural number and x â‰¤ 4}

A={1,2,3,4}

The number of elements in this set is four.

This is a finite number. Sets having a finite number of elements are known as non-empty finite sets.

**Non-empty Finite Set:** If the number of elements in a set S is a natural number, then S is said to be Non-empty Finite Set.

Consider a set that does not contain any element.

E = {x: x is a real solution of x^{2} + 1 = 0}

This set consists of elements that are real roots of the equation x square plus one is equal to zero.

x^{2} + 1 = 0

x^{2} = -1

**Empty Set**: A set that does not contain any element is called an Empty Set or Null Set or a Void Set.

E = {} = âˆ…

An empty set is denoted by the symbol â€” phi.

A = {1, 2, 3, 4}

E = {} = âˆ…

**Infinite Set:** A set that is empty or consists of a definite number of elements is called Finite Set, otherwise it is called an Infinite Set.

**N = {x: x is a natural number}
N = {1,2,3,4,...}
X = {a: a is solution of a**

Sets X and Y are equal since both have the same number of elements as well as the same type of elements.

**Equal Sets:** Two sets A and B are said to be equal if they have exactly the same elements and we write A=B. Otherwise, the sets are said to be unequal and we write **A â‰ B**.

**A = {1,2,3,4}** and **B = {a,b,c,d}**

Elements of these two sets are different. So, these sets are not equal to each other.