Question

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find 

i. A x (B ∩ C) 

ii. (A x B) ∩ (A xC) 

iii. A x (B ∪ C) 

iv. (A x B) ∪ (A x C)

Answer 1

Given : A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6} 

(i) To find : A × (B ∩ C)

 (B ∩ C) = {4} 

∴ A × (B ∩ C) = {(1, 4), (2, 4), (3, 4)} 

(ii) To find : (A × B) ∩ (A × C) 

(A × B) = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)} 

(A × C) = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

∴ (A × B) ∩ (A × C) = {(1, 4), (2, 4), (3, 4)} 

(iii) To find : A × (B ∪ C)

 (B ∪ C) = {3, 4, 5, 6} 

∴ A × (B ∪ C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)} 

(iv) To find : (A × B) ∪ (A × C) 

(A × B) = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)} 

(A × C) = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)} 

∴ (A × B) ∪ (A × C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}