Question

If A and B are subsets of the universal set U, then which of the following is/are true?

• A. A ⊂ (A ∪ B)
• B. A ⊂ B ⇔ (A ∪ B) = B
• C. (A ∩ B) ⊂ A
• D. A - B = (A ∪ B')

Answer 1

Answer: (A), (B), (C)

(A ∩ B) ⊂ A

A ⊂ (A ∪ B) is true as A ∪ B is a collection of all elements of A and B, hence A is a subset of A ∪ B.

A ⊂ B ⇔ (A ∪ B) = B is true. If A is a subset of B, then all elements of A are elements of B also. Hence (A ∪ B) = B.
If (A ∪ B) = B, this means collection of all the elements of set A and B are in set B. Therefore, all the elements of set A are also element of set B. Hence, A ⊂ B

(A ∩ B) ⊂ A is true as A ∩ B is a collection of elements common to both set A and set B. Hence, elements in A ∩ B will always be present in both set A and set B. Hence, (A ∩ B) is a subset of A.

A - B = (A ∪ B') is false as A - B = (A ∩ B')