Question

If A is subset of B then find A intersection B , A union B ,A-B

Answer 1

Step-by-step explanation:

The trivial case first: If A⊆B and A=∅, then A∩B=∅=A. Conversely, if A∩B=A and A=∅, then A⊆B, since ∅ is a subset of every set.

Now, suppose A≠∅. Suppose A⊆B. If x∈A, then , from the definition of subset. Thus,  and . Therefore, by the definition of intersection of sets, . Therefore, every  in  is in . From the definition of containment, . Each element of  is in both  and , so . Since  and , the definition of set equality gives . For the converse. If , then since , . Q.E.D.

Now, write it up nicely in your own hand before turning it in.