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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Indicate whether the statement in parts (a)-(d) are true or false for all functions. Justify your answers.

  1. If two elements in the domain of a function are equal, then their images in the co-domain are equal.

  • If two elements in the co-domain of a function are equal, then their preimages in the domain are also equal.
  • A function can have the same output for more than one input.
  • A function can have the same input for more than one output.
  • To determine

    (a)

    Indicate whether the statements are true or false.

    If two elements in the domain of a function are equal, then their images in the co-domain are equal.

    Explanation

    Given information:

    If two elements in the domain of a function are equal, then their images in the co-domain are equal.

    Concept used:

    Different elements only have to be matched to different images.

    Calculation:

    If two elements in t...

    To determine

    (b)

    If two elements in the co—domain of a function are equal, then their preimages in the domain are also equal.

    To determine

    (c)

    The given statement is true or false.

    A function can have the same output for more than one input.

    To determine

    (d)

    A function can have the same input for more than one output.

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