Question

For the nonempty sets \( A \) and \( B \), which of the following is NOT true? \( \overline{A} \) is the complement of A

• A. \( A \cap (\overline{A} \cup B) = A \cap B \)
• B. \( A \cup (\overline{A} \cap B) = A \cup B \)
• C. \( A - (A - B) = B \)
• D. \( A \cup (B - A) = A \cup B \)

Hint:

To validate set identities, simplify the expressions by applying set operations and see if both sides of the equation match.

Answer 1

The Correct Option is C

- Option (3) is incorrect because \( A - (A - B) \) results in \( B \cap A \), not \( B \) directly.
- The other options are valid set identities based on set theory operations.