Show that A × (B ∩ C) = (A × B) ∩ (A × C). Where A= {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}
Question
Solution 1
To show that A × (B ∩ C) = (A × B) ∩ (A × C), we need to prove that the two sets are equal.
First, let's find A × (B ∩ C):
A × (B ∩ C) = {(1, x) | x ∈ (B ∩ C)}
Since B ∩ C = {}, the intersection of B and C is empty. Therefore, A × (B ∩ C) is also empty.
Next, let's find (A × B) ∩ (A × C):
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