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Math Help - Proof: cardinalities of sets

  1. #1
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    Proof: cardinalities of sets

    Let a be the common cardinality of sets A and C. Let b be the size of B. If C is a subset of B, then a<= b.

    I understand why this is true, but how do I give a solid proof?

    Thanks.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jzellt View Post
    Let a be the common cardinality of sets A and C. Let b be the size of B. If C is a subset of B, then a<= b.

    I understand why this is true, but how do I give a solid proof?

    Thanks.
    note that if C \subseteq B, then |C| \le |B| (you can prove this by contradiction).

    here, since |A| = |C|, we have |A| \le |B|
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