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

**Jessica.M** · May 27th 2008, 05:42 AM

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.

**Plato** · May 27th 2008, 07:56 AM

If $f:A \mapsto B\,\& \,g:B \mapsto C$ then what do you know about $g \circ f$ ?

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

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