What is a function in terms of a relation?
What is a function in terms of a relation?
Answer: A. A relation where every element of the domain is related to exactly one element of the codomain — Definition: In terms of relations, a function is a special type of relation that assigns to every element of the domain exactly one element of the codomain.…
- A.
A relation where every element of the domain is related to exactly one element of the codomain
- B.
A relation where some elements of the domain are related to more than one element of the codomain
- C.
A relation where every element of the domain is related to at least one element of the codomain
- D.
A relation where some elements of the domain are not related to any element of the codomain
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Correct answer: A
Definition: In terms of relations, a function is a special type of relation that assigns to every element of the domain exactly one element of the codomain.
Key requirement: each input (domain element) has one and only one output (codomain element).
Not a function if any input has zero outputs or more than one output.
Example of a function: the relation { (1,2), (2,3), (3,2) } where each domain element 1, 2, 3 maps to exactly one value.
Non-function examples: { (1,2), (1,3) } (input 1 maps to two outputs) and domain {1,2} with relation { (1,2) } (input 2 has no output).
Therefore, the correct definition is a relation where every domain element is related to exactly one codomain element.