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Sets and Functions

  • A set is a well-defined collection of objects.
  • Sets are usually represented by capital letters A, B, C, D, X, Y, Z, etc. The objects inside a set are called elements or members of a set. They are denoted by small letters a, b, c, d, x, y, z, etc.
  • If a is an element of a set A, then we say that “a belongs to A” and mathematically we write it as “aA”; if b is not an element of A, then we write “bA”.
  • There are three different ways of representing a set:
    • Description method: Description about the set is made and it is enclosed in curly brackets { }.

For example, the set of composite numbers less than 30 is written as follows:

{Composite numbers less than 30}

    • Roster method or tabular form: Elements are separated by commas and enclosed within the curly brackets { }.

For example, a set of all integers greater than 5 and less than 9 will be represented in roster form as {6, 7, 8}. 

    • Set-builder form or rule method: All the elements of the set have a single common property that is exclusive to the elements of the set i.e., no other element outside the set has that property.

For example, a set L of all integers greater than 5 and less than 9 in set-builder form can be represented as follows:

L = {x : x is an integer greater than 5 and less than 9}

  • Some important points:
    1. The order of listing the elements in a set can be changed.
    2. If one or more elements in a set are repeated then the set remains the same.
    3. Each element of the set is listed once and only once.
  • On the basis of number of elements, sets can be classified as:
    • Finite set − A set that contains limited (countable) number of different elements is called…

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