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

1. ## 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.

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