Question

If A = {2, 3}, B = {4, 5}, C ={5, 6}, find A × (B ∪ C), A × (B ∩ C), (A × B) ∪ (A × C).

Answer 1

Given:
A = {2, 3}, B = {4, 5} and C ={5, 6}
Also,
(B ∪ C) = {4, 5, 6}
Thus, we have:
A × (B ∪ C) = {(2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3,6)}
And,
(B ∩ C) = {5}
Thus, we have:
A × (B ∩ C) = {(2, 5), (3, 5)}
Now,
(A × B) = {(2, 4), (2, 5), (3, 4), (3, 5)}
(A × C) = {(2, 5), (2, 6), (3, 5), (3, 6)}
∴ (A × B) ∪ (A × C) = {(2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}