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

As per given question,
(B ∪ C) = {b, c, e} ∪ {b, c, f} = {b, c, e, f}
∴ A × (B ∪ C) = {a, d} × {b, c, e, f}
= {(a, b), (a, c), (a, e), (a, f), (d, b), (d, c), (d, e), (d, f)} …...........(1)
Also, (A × B) = {(a, b), (a, c), (a, e), (d, b), (d, c), (d, e)}
and, (A × C) = {(a, b), (a, c), (a, f), (d, b), (d, c), (d, f)} …............(2)
∴ (A × B) ∪ (A × C) = {(a, b), (a, c), (a, e), (a, f), (d, b), (d, c), (d, e), (d, f)}
From (1) and (2), we have
A × (B ∪ C) = (A × B) ∪ (A × C).