Question

For 2 sets A and B, which of the following is/are true always?

• A. A - B = {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

Answer: (A), (B)

The correct options are
A

A - B = {x : x ∈ A and x ∉ B}

B

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

(a) A - B is the set in which elements belong to A, but does not belong to B. So, A - B = {x : x ∈ A and x ∉ B}.

(b)

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

(c) As A - B and B - A are disjoint sets, A - B ≠ B - A always.

(d) A ∪ B = {x : x ∈ A or x ∈ B}

So, only first two options are true.