The "set by description" 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. It provides a concise and formal way to define a set without explicitly listing all its elements. Set-builder notation typically uses the following format:

                 {variable | condition}

  • Variable:- This is a placeholder for the elements of the set. It represents the general form that elements of the set should take.
  • Condition:- This is 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 some examples of sets represented using set-builder notation:

  1. The set of all positive integers less than 10:- {x | x is a positive integer and x < 10}. In this example, "x" is the variable representing elements, and the condition specifies that these elements should be positive integers less than 10.
  2. The set of even numbers:-  {n | n is an integer, and n is even}. Here, "n" represents the elements of the set, and the condition restricts them to integers that are even.
  3. The set of all uppercase letters in the English alphabet:- {letter | letter is an uppercase English letter}. In this case, "letter" represents the elements, and the condition specifies that they should be uppercase letters.
  4. The set of all multiples of 5:- {m | m is an integer, and m is a multiple of 5} "m" is the variable representing elements, and the condition requires that these elements be integers that are multiples of 5.

Set-builder notation allows you to define sets in a more abstract and general way, making it useful for describing sets with infinite or large numbers of elements, or sets with specific properties.