Table of Contents
Relations and Functions class 11
Explain the difference between a relation and a function.
A relation is a set of ordered pairs. A function is a relation in which each element in the domain is paired with one and only one element in the range.
What is a Function?
A function is a relation that describes there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
For example:
| Domain | Range |
| -1 | -3 |
| 1 | 3 |
| 3 | 9 |
| Domain | It is a collection of the first values in the ordered pair (Set of all input (x) values). |
| Range | It is a collection of the second values in the ordered pair (Set of all output (y) values). |
Example:
In the relation, {(-2, 3), {4, 5), (6, -5), (-2, 3)},
The domain is {-2, 4, 6} and range is {-5, 3, 5}.
Note: Don’t consider duplicates while writing the domain and range and also write it in increasing order.
Types of Functions
In terms of relations, we can define the types of functions as:
- One-to-one function or Injective function: A function f: P → Q is said to be one-to-one if for each element of P there is a distinct element of Q.
- Many-to-one function: A function that maps two or more elements of P to the same element of set Q.
- Onto Function or Surjective function: A function for which every element of set Q there is a pre-image in set P
- One-one correspondence or Bijective function: The function f matches with each element of P with a discrete element of Q and every element of Q has a pre-image in P.
Explain in Detail: Cartesian Products of Sets
A Cartesian product of two sets is a set that is created by pairing every element of the first set with every element of the second set. For example, if the first set consists of the numbers 1, 2, and 3, and the second set consists of the numbers 4, 5, and 6, the Cartesian product of the two sets would be the set {1, 4, 2, 5, 3, 6}.
