Let A = {1, 2, 3}, B = {3, 4 and C = {4, 5, 6}. Find (i) A × (B ∩

1.	Let A = {1, 2, 3}, B = {3, 4 and C = {4, 5, 6}. Find (i) A × (B ∩ C) (ii) (A × C) ∩ (A × C)
Answer» 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)}

Let A = {1, 2, 3}, B = {3, 4 and C = {4, 5, 6}. Find (i) A × (B ∩ C) (ii) (A × C) ∩ (A × C)

Answer»

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)}