If A = {a, d}, B = {b, c, e} and C = {b, c, f}, then A ×

Home » Aptitude » Sets and Functions » Question

If A = {a, d}, B = {b, c, e} and C = {b, c, f}, then A × (B ∩ C) =

1. ϕ
2. (A × B) ∩ (A × C)
3. (A × B) ∪ (A × C)
4. None of these

Correct Option: B

Given in the question, we can can calculate,
(B ∩ C) = {b, c, e} ∩ {b, c, f} = {b, c}
∴ A × (B ∩ C) = {a, d} × {b, c}
= {(a, b), (a, c), (d, b), (d, c)}
Also, (A × B) ∩ (A × C)
= {(a, b), (a, c), (a, b), (d, c)}
∴ A × (B ∩ C) = (A × B) ∩ (A × C).