Difference between Relation and Function
The difference between relation and function is given below:
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Relation |
Function |
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A relation is a set of ordered pairs, where each pair consists of two elements, establishing a relationship between them. |
A function is a special type of relation where each input value (domain) is associated with exactly one output value (range). |
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A single input can be related to multiple outputs. |
Each input is associated with only one output. |
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The relationship between elements doesn’t guarantee a unique output for each input. |
Every input has a precisely defined output. |
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Represented as a set of ordered pairs. |
Represented as a mapping from domain to range. |
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Often denoted as R, where R ⊆ A × B, with A and B being sets |
Denoted as f: A → B, where f is the function, A is the domain, and B is the range. |
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If R = {(1, 2), (2, 3), (3, 4)}, it represents a relation between elements where each element is related to the next one. |
If f(x) = x2, it represents a function where each input x is associated with its square as the output. |
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A relation is a broader concept that includes functions as a special case. |
Functions are a specific type of relation with stricter rules regarding output associations. |
Difference between Relation and Function
Relation defines how elements of one set relate to elements of another set whereas a Function is a special type of relation in which each element in the domain (input) is related to exactly one element in the codomain (output).
This article explores relations and functions, highlighting their definitions, properties, differences, and applications in mathematics.