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

• May 27th 2008, 06:42 AM
Jessica.M
Prove that if |A| ≤ |B| and |B| ≤ |C| then |A| ≤ |C| (Cardinality)
Hello,
Can someone do this question please ? I can't do it. http://www.mymathforum.com/images/smiles/icon_sad.gif

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. http://www.mymathforum.com/images/smiles/icon_sad.gif
• May 27th 2008, 08:56 AM
Plato
If $f:A \mapsto B\,\& \,g:B \mapsto C$ then what do you know about $g \circ f$?