Question

For sets A and B, n(A) = 3, n(A x (B – A)) = 6, then n(B) cannot be

• A. 3
• B. 6
• C. 2
• D. 4

Answer 1

Answer: (B)

6

Answer 2

Explanation:

1. Given Information:

   • n(A) = 3
   • n(A x (B – A)) = 6

2. Cartesian Product Formula: n(A x (B – A)) = n(A) * n(B – A)

3. Calculate n(B – A): 6 = 3 * n(B – A) n(B – A) = 2

4. Relate n(B) to n(B – A) and n(A ∩ B): n(B) = n(A ∩ B) + n(B – A)

5. Possible values for n(A ∩ B): Since (A ∩ B) is a subset of A, n(A ∩ B) ≤ n(A) = 3. Also, n(A ∩ B) ≥ 0. Thus, n(A ∩ B) can be 0, 1, 2, or 3.

6. Calculate possible values for n(B):

   • If n(A ∩ B) = 0, then n(B) = 0 + 2 = 2.
   • If n(A ∩ B) = 1, then n(B) = 1 + 2 = 3.
   • If n(A ∩ B) = 2, then n(B) = 2 + 2 = 4.
   • If n(A ∩ B) = 3, then n(B) = 3 + 2 = 5.

   Therefore, possible values for n(B) are 2, 3, 4, and 5.

7. Compare with the given options: The value 6 is not a possible value for n(B).