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Introduction to Relations and Functions

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Questions and Answers

What is the key distinction between relations and functions?

Relations can have multiple inputs for a single output, while functions have a one-to-one correspondence between inputs and outputs. (correct)
Relations are always reflexive, symmetric, and transitive, while functions do not have these properties.
Relations are always represented graphically, while functions can be represented in various forms.
Relations are sets of ordered pairs, while functions are sets of ordered triples.

Which type of relation is both reflexive and symmetric?

Equivalence relation (correct)
Symmetric relation
Reflexive relation
Transitive relation

What is the relationship between one-to-one (injective) functions and bijective functions?

One-to-one functions and bijective functions are the same type of function.
Bijective functions are a subset of one-to-one functions.
One-to-one functions are a subset of bijective functions. (correct)
One-to-one functions and bijective functions are mutually exclusive.

Which type of function has the property that every element in the codomain is the image of at least one element in the domain?

Onto (surjective) function (B) Signup and view all the answers

What is the notation for a composite function?

(f ∘ g)(x) = f(g(x)) (D) Signup and view all the answers

What is the purpose of function composition?

To apply one function to the result of another function. (D) Signup and view all the answers

What is a binary operation?

A function that operates on pairs of elements from the same set, producing another element of the same set. (C) Signup and view all the answers

How can functions be represented pictorially?

Using Cartesian coordinates and mapping diagrams. (D) Signup and view all the answers

Which condition is necessary for a function to be invertible?

The function must be both one-to-one and onto. (C) Signup and view all the answers

What is a real-world application of composite functions?

Determining the cost of production in economics. (D) Signup and view all the answers