Note that as (i) implies that A is a subset of B, then it follows that the intersection of B with A equals A, and it also follows that the union of A with B is B. The other way round : if the union of A with B is B, then A must be a subset of B, and it follows that the intersection of B with A equals A.

To help understand this, draw a diagram with and

Once you will have understood why this works, you will be able to put it in mathematical terms.

Here are some basic ideas that can help you, too :

If A is a subset of B, it means that all the elements of A are contained in B, among other elements of B

If A intersect B = A, it means that the only elements that are in A and in B are the elements of B (equivalent to : A is a subset of B)

If A union B = B, it means that the elements that are in A or in B, are equal to the elements of B (equivalent to : A is a subset of B)