Question

Let A = {1, 2, 3}, B = {3, 4 and C = {4, 5, 6}. Find 

(i) A × (B ∩ C) 

(ii) (A × C) ∩ (A × C) 

Answer 1

A {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, B ∩ C = {4} 

(i) A × (B ∩ C) 

= {1, 2, 3} × {4} 

= {(1, 4), (2, 4), 3, 4)} 

(ii) (A × B) ∩ (A × C) 

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

= {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)} 

∩ {(1, 4), 1, 5), (1, 6), (2, 4), (2, 5), 

(2, 6), (3, 4), (3, 5), (3, 6)} 

= {(1, 4), (2, 4), (3, 4)}