A **set **is a well-defined collection of distinct elements. Sets are typically denoted by uppercase letters, and their elements are enclosed within curly braces

Each individual object within a set is known as an element.

In set A, the elements are 1, 2, 3, 4, and 5 and in set B, the elements are "apple," "mango," and "orange."

The number of elements in a set is called its cardinality. The cardinality of a set is denoted by vertical bars.

For set

Sets are unordered collections of elements. This means that the arrangement of elements within a set does not matter. For example, the sets

Sets can indeed be represented in any one of the following three ways or forms:

Descriptive form

Set-builder form

Roster or tabular form

In the descriptive form, a set is described in words and specified by providing a verbal description of its elements, making it easy to know which items are part of the set and which are not.

Set-builder notation, also known as the rule form, is a notation used to describe a set by indicating the properties or conditions that its members must satisfy.

The symbol

$|$ or$:$ stands for "such that."

In the roster form, a set is represented by listing all its elements inside a pair of braces

Note:You can learn more about

The commutative property applies to both union and intersection operations.

The associative property applies to both union and intersection operations.

The distributive property applies to both union and intersection operations.

The identity property applies to both union and intersection operations.

The complement property applies to both union and intersection operations.

The idempotent property applies to both union and intersection operations.

In conclusion, sets form the foundation of various mathematical concepts and operations. They are useful in solving problems across various fields, such as probability, logic, and computer science.

Match The Answer

Select an option from the left-hand side

Set-builder notation

Number of elements in a set

Roster form

Describing a set using conditions

Cardinality

$X = \{2, 4, 6, 8\}$

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