Question

\((A-B)∪(B-A)=\)

• A. \(A∪B\)
• B. \(A∩B\)
• C. \(\phi\)
• D. \((A∪B)-(A∩B)\)

Answer 1

The Correct Option is D

We are given the expression \( (A - B) \cup (B - A) \), which represents the union of two sets:
\( A - B \) refers to the elements in \( A \) but not in \( B \),
\( B - A \) refers to the elements in \( B \) but not in \( A \). The union of these two sets includes all elements in \( A \) that are not in \( B \), plus all elements in \( B \) that are not in \( A \). Now, the expression \( (A \cup B) - (A \cap B) \) gives us all elements in either \( A \) or \( B \), except the elements that are in both \( A \) and \( B \) (i.e., the intersection). Thus, the solution simplifies to: \[ (A - B) \cup (B - A) = (A \cup B) - (A \cap B) \]

The correct option is (D): \((A∪B)-(A∩B)\)