Question

Let A, B be sets. Show that if B is finite and A is a subset of B then A is finite as well

Answer 1

I know that if B is finite then it is an empty set of B~{1,...,n} for some n in N.
A is a subset of B if there exists an x in A and x in B
But how do I use this to prove that A is also finite

Answer 2

Well if B~{1,2,..,n}
then |B|=n.
We know have the following: