Question

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

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

Hint:

Always write out Cartesian products explicitly when unsure—it’s easy to miss ordered pair details.

Answer 1

The Correct Option is D

We compute: \[ A \times B = \{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(5,1),(5,2),(5,3),(6,1),(6,2),(6,3)\} \] \[ B \times A = \{(1,1),(1,2),(1,5),(1,6),(2,1),(2,2),(2,5),(2,6),(3,1),(3,2),(3,5),(3,6)\} \] Their intersection: only elements common to both \[ C = \{(1,1),(1,2),(2,1),(2,2)\} \] Thus, (2,3) ∉ C → it's the incorrect one.