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Difficulty: 2/102024 NMTC 2024 (QII-49)

Which of the following relations is NOT a mathematical function?

Options:

  • A one-to-many relation

  • B.

    A one-to-one relation

  • C.

    A many-to-one relation

  • D.

    An identity relation

Guide / Hint

Hint 1: Recall the fundamental definition of a function: each input must map to exactly one output.

Hint 2: Consider which relation type allows a single input to map to multiple different outputs.

Hint 3: Identify that a 'one-to-many relation' violates this rule, which corresponds to option index 0.

Solution

Step 1 (Definition of a Function): A mathematical function is a relation that assigns to each element of the domain exactly one element of the codomain .

Step 2 (Analyze one-to-many relation): In a one-to-many relation, a single input value in is mapped to multiple distinct output values in . This violates the core definition of a function (which requires a single, unique output for each input).

Step 3 (Conclusion): A one-to-many relation is not a function. This corresponds to option index 0.

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