- #1

angela107

- 35

- 2

- Homework Statement:
- Is it TRUE that for all sets ##A## and ##B## the identity ##A \setminus (A \setminus B) =A ∩ B## holds?

- Relevant Equations:
- n/a

##A ∖ B## can't include any elements that are not in ##A##, so it is the same as saying ##A∖(A∩B)##; it's exactly the elements of ##A## except those in ##A∩B##.

##A∖(A∖(A∩B))## is exactly the elements of ##A## except those in (exactly the elements of ##A## except those in ##A∩B##). This is the same as ##A∩B##.

Therefore, it is true that for all sets A and B the identity ##A ∖ (A ∖B) =A ∩ B##holds.

Is this correct?

##A∖(A∖(A∩B))## is exactly the elements of ##A## except those in (exactly the elements of ##A## except those in ##A∩B##). This is the same as ##A∩B##.

Therefore, it is true that for all sets A and B the identity ##A ∖ (A ∖B) =A ∩ B##holds.

Is this correct?