Introduction to Relations and Functions
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Introduction to Relations and Functions

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@PreciseLute

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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?

    <p>Onto (surjective) function</p> Signup and view all the answers

    What is the notation for a composite function?

    <p>(f ∘ g)(x) = f(g(x))</p> Signup and view all the answers

    What is the purpose of function composition?

    <p>To apply one function to the result of another function.</p> Signup and view all the answers

    What is a binary operation?

    <p>A function that operates on pairs of elements from the same set, producing another element of the same set.</p> Signup and view all the answers

    How can functions be represented pictorially?

    <p>Using Cartesian coordinates and mapping diagrams.</p> Signup and view all the answers

    Which condition is necessary for a function to be invertible?

    <p>The function must be both one-to-one and onto.</p> Signup and view all the answers

    What is a real-world application of composite functions?

    <p>Determining the cost of production in economics.</p> Signup and view all the answers

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