CLASS-6
SET REPRESENTATION BY SET BUILDER METHOD

SET REPRESENTATION BY SET BUILDER METHOD -

The set-builder method, also known as set-builder notation, is a way to represent a set by describing the characteristics or properties that its elements must satisfy. This notation uses the format {variable | condition}, where:

• Variable:- Represents a placeholder for the elements of the set. It describes the general form that elements of the set should take.
• Condition:- Specifies a statement or criterion that describes the specific properties or characteristics that elements in the set must meet. It serves as a filter to determine which elements belong to the set.

Here are a few examples of sets represented using the set-builder method:

Example 1:- Set of Even Numbers

        { x | x is an integer and x is even }

In this example, "x" is the variable representing the elements of the set. The condition specifies that the elements are integers (denoted by "x is an integer") and that they must be even numbers.

Example 2:- Set of Prime Numbers Less Than 20.

        { p | p is a prime number and p < 20 }

Here, "p" represents the elements of the set. The condition restricts the elements to prime numbers (denoted by "p is a prime number") that are less than 20.

Example 3:- Set of Vowels in the English Alphabet.

        { letter | letter is a vowel in the English alphabet }

In this case, "letter" is the variable representing the elements, and the condition specifies that the elements must be vowels in the English alphabet.

Example 4:- Set of Positive Real Numbers.

        { x | x is a real number and x > 0 }

This set includes positive real numbers. "x" represents the elements, and the condition ensures that the elements are real numbers greater than 0.

The set-builder method allows you to define sets in a concise and abstract manner, making it suitable for specifying sets with specific properties or characteristics, especially when listing all elements explicitly would be impractical or impossible.