Is this statement true or false: If n(A)is greater than or less than n(B), then A is a subset of B.?

I think the answer is true but I am not sure how to explain it.Is this statement true or false: If n(A)is greater than or less than n(B), then A is a subset of B.?
For a start n(A) cannot both be greater than AND less than n(B). It must be one or the other





Also, It depends on the elements that make up the sets of A and B.


If all of the elements in A are contained in B and there are elements in B that do not belong to A then n(A) %26lt; n(B) and A is a 'proper' subset of B.





If all the elements of A are contained in B and all of the elements in B are contained in A, then A = B, n(A) = n(B) and both are subsets of each other, although not proper subsets.





If there are some elements in A that do not belong to B and


n(A) %26lt; n(B), then even though the cardinality of A is less than


B, A is NOT a subset of B. However there exists an intersection of elements that form a proper subset of both A and B.





In short, a set of elements A is a subset of another set B if and only if all of those elements in A are contained in (or are members of) the set B. In which case n(A) %26lt;= n(B). It does not necessarily follow that if


n(A) %26lt;= n(B), then A is a subset of B, since there may exist elements in A that do not belong to B.