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.

Quote:

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Originally Posted by jzellt

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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note that if , then (you can prove this by contradiction).

here, since , we have