If A = {2, 3},
Question:

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

Solution:

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)}

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