Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine (i) A × B (ii) B

1.	Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine (i) A × B (ii) B × A (iii) Is A × B = B × A ? (iv) Is n (A × B) = n (B × A) ?
Answer» Since A = {1, 2, 3, 4} and B = {5, 7, 9}. Therefore, (i) A × B = {(1, 5), (1, 7), (1, 9), (2, 5), (2, 7), (2, 9), (3, 5), (3, 7), (3, 9), (4, 5), (4, 7), (4, 9)} (ii) B × A = {(5, 1), (5, 2), (5, 3), (5, 4), (7, 1), (7, 2), (7, 3), (7, 4), (9, 1), (9, 2), (9, 3), (9, 4)} (iii) No, A × B ≠ B × A. Since A × B and B × A do not have exactly the same ordered pairs. (iv) n (A × B) = n (A) × n (B) = 4 × 3 = 12 n (B × A) = n (B) × n (A) = 4 × 3 = 12 Hence n (A × B) = n (B × A)

Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine (i) A × B (ii) B × A (iii) Is A × B = B × A ? (iv) Is n (A × B) = n (B × A) ?

Answer»

Since A = {1, 2, 3, 4} and B = {5, 7, 9}. Therefore,

(i) A × B = {(1, 5), (1, 7), (1, 9), (2, 5), (2, 7), (2, 9), (3, 5), (3, 7), (3, 9), (4, 5), (4, 7), (4, 9)}

(ii) B × A = {(5, 1), (5, 2), (5, 3), (5, 4), (7, 1), (7, 2), (7, 3), (7, 4), (9, 1), (9, 2), (9, 3), (9, 4)}

(iii) No, A × B ≠ B × A. Since A × B and B × A do not have exactly the same ordered pairs.

(iv) n (A × B) = n (A) × n (B) = 4 × 3 = 12

n (B × A) = n (B) × n (A) = 4 × 3 = 12

Hence n (A × B) = n (B × A)