If A and B are two non-empty disjoint sets then (A-B)∩B = ____?
- A∩B
- AUB
- ∅
- None of these
Explanation
A - B (set difference) is the set of elements that are in A but not in B. So, A - B = { x | x ∈ A and x ∉ B }.
Since A and B are disjoint (no common elements), every element of A is not in B. Therefore, A - B = A.
So, (A - B) = A.
Now, we need (A - B) ∩ B = A ∩ B.
But since A and B are disjoint, A ∩ B = ∅.
Therefore, (A - B) ∩ B = ∅.
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