What are Equivalent Sets and Equal Sets | Types of Sets | MathOGuide

What are Equivalent Sets and Equal Sets | Types of Sets | MathOGuide

Equivalent sets and equal sets are concepts in set theory:

1. **Equal Sets**: Two sets are equal if they have exactly the same elements. For example, if set A = {1, 2, 3} and set B = {1, 2, 3}, then A = B because they contain the same elements.

2. **Equivalent Sets**: Two sets are equivalent if they have the same number of elements. In other words, if you can establish a one-to-one correspondence between the elements of one set and the elements of another set. For example, set A = {1, 2, 3} and set B = {4, 5, 6} are equivalent because both sets contain three elements.

Types of Sets:
- **Finite Set**: A set that contains a definite number of elements.
- **Infinite Set**: A set that contains an unlimited number of elements.
- **Singleton Set**: A set that contains only one element.
- **Empty Set (Null Set)**: A set that contains no elements.