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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

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}.

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Solution

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):

(A ×

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This problem has been solved

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