Question

Find the dual of A U (B U C).

Answer 1

A U (B U C) = (A U B) U C = A U C = A
or
A U (B U C) = A U (C U B) = (A U C) U B = A U B = A

Either way we get set A as an answer.

Answer 2

Answer:

    The answer is A U (B U C) =  (A ∩ B) ∪ (A ∩ C).

Step-by-step explanation:

• Suppose x ∈ A∩(B ∪C), then x ∈ A and x ∈ B ∪C. The latter means that either x ∈ B or x ∈ C.
• If x ∈ B, then x ∈ A ∩ B, and if x ∈ C, then x ∈ A ∩ C.
• Thus, either x ∈ A ∩ B, or x ∈ A ∩ C, i. e. x ∈ (A ∩ B) ∪ (A ∩ C).