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Math Help - surjective

  1. #1
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    surjective

    Some surjective functions from A to B are not injective( Here A and B are variables representing two sets. The universe is the set of all functions from A to B)

    What would the open sentence using quanitifiers for this statement be.

    there exists 2 elements in A such that if there exists an element of A for all elements of B then 2 elements of B are equal and the corresponding elements in a are not equal
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  2. #2
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    Quote Originally Posted by leinadwerdna View Post
    Some surjective functions from A to B are not injective( Here A and B are variables representing two sets. The universe is the set of all functions from A to B)

    What would the open sentence using quanitifiers for this statement be.

    there exists 2 elements in A such that if there exists an element of A for all elements of B then 2 elements of B are equal and the corresponding elements in a are not equal
    That sentence is nonsense.
    Please check the source and edit it so it is exactly as you find it in the source.
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  3. #3
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    Well, this phrase is an attempted answer, not the problem statement.

    Your sentence starts with "there exists 2 elements in A", but "Some surjective functions" is talking about functions from A -> B, not elements of A.

    The outline of the sentence is: There exist a function f such that f is surjective and f is not injective. Then you may need to expand the definitions of "surjective" and "injective".
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