Question

Let \( A = \{1, 2, 5, 6\} \), \( B = \{1, 2, 3\} \), and \( C = (A \cap B) \cup (B \cap A) \). Which of the following is INCORRECT?

• A. \( (1, 2) \in C \)
• B. \( (1, 1) \in C \)
• C. \( (2, 2) \in C \)
• D. \( (2, 3) \in C \)

Hint:

When working with set operations, always first identify the common elements and intersections before determining the elements of other sets.

Answer 1

The Correct Option is D

We are given the sets \( A \), \( B \), and \( C \), where \( C = (A \cap B) \cup (B \cap A) \). The intersection of \( A \) and \( B \) is \( A \cap B = \{ 1, 2 \} \), so \( C = \{ 1, 2 \} \). Thus, \( (2, 3) \) is not an element of \( C \), making option (4) incorrect.