Question

Consider two sets A and B, which of the following is always true?

• A. B - A = {x: x ∈ A and x ∉ B}
• B. The sets A - B, A ∩ B and B - A are mutually disjoint sets.
• C. A - B = B - A
• D. A ∪ B = {x: x ∈ B and x ∉ A}

Answer 1

The correct option is B

The sets A - B, A ∩ B and B - A are mutually disjoint sets.

(a) A - B is the set in which elements belongs to A but not belong to B.

So, A - B = {x: x $\in$ A and x $\notin$ B} $\ne$ B - A

(b)

So, A - B, A $\cap$ B and B - A are mutually disjoint sets

(c) As A - B and B - A are disjoint sets, A - B $\ne$ B - A always.

(d) A $\cup$ B = {x:x $\in$ A or x $\notin$ B}