Sets,Relations and Functions

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What is a set?

Back

A set is a collection of distinct objects, considered as an object in its own right. For example, A = {1, 2, 3} is a set.

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What is a function?

Back

A function is a relation that assigns exactly one output for each input. For example, f(x) = x^2 is a function.

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What is the domain of a function?

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The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.

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How do you determine if a relation is a function?

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A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

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What is a mapping?

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A mapping is a way to describe how each element of one set (domain) is paired with an element of another set (range).

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What is n(A) in set theory?

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n(A) represents the number of elements in set A. For example, if A = {1, 2, 3}, then n(A) = 3.

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What is an ordered pair?

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An ordered pair is a pair of elements (a, b) where the order matters. For example, (1, 2) is different from (2, 1).

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.

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What does it mean for a function to be one-to-one?

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A one-to-one function is a function where each output is produced by exactly one input, meaning no two different inputs map to the same output.