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Math Help - Prove that if |A| ≤ |B| and |B| ≤ |C| then |A| ≤ |C| (Cardinality)

  1. #1
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    Unhappy Prove that if |A| ≤ |B| and |B| ≤ |C| then |A| ≤ |C| (Cardinality)

    Hello,
    Can someone do this question please ? I can't do it.

    Prove that if |A| ≤ |B| and |B| ≤ |C| then |A| ≤ |C|

    Note: |A| ≤ |B| means "there exist an injection from set A into set B" and so on for the rest.


    I would really appreciate it if someone can help me because I find this very hard.
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    If f:A \mapsto B\,\& \,g:B \mapsto C then what do you know about g \circ f?
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