Prove that if A is a subset of B, then .
Can I just since |A| less than or equal to |B|, <A> is a subgroup of <B>?
Frankly what you have written makes little sense. If A and B are sets then " " is meaningless because there is no operation in a set. Apparently you are talking about groups, not sets. But even then you have to define <A>. You appear to mean a sub-group generated by a single element of the group but which element? Or are you assuming from the start that A and B are themselves generated by a single element?