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## Given sets A and B, prove that A is a subset of B (Apostol)

1. The problem statement, all variables and given/known data

Continuing with my Apostol efforts. From Section I 2.5:

These exercises go over some of the absolute basics of sets. In 3. I'm given A = {1}, B = {1,2} and asked to decide whether some statements are true or false, proving the ones that are true. Seeing which ones are true is no problem but I have no idea what the proper way to 'prove' them might be. For example, How do I prove that A is a subset of B

3. The attempt at a solution

Assume A is a subset of B, then for any x in A, x is in B...no idea

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Another question (6.) gives us A = {1,2} and C = {{1}, {1,2}} and it asks if A is an element of C if so to prove it. I see that it is but once again have no idea how to prove it.
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