If $A = \{1, 2, 3\}$, $B = \{3, 4\}$, $C = \{4, 5, 6\}$, then $A \times (B \cap C)$ equals:
A$\phi$
B$\{(1,3), (2,3), (3,3)\}$
C$\{(1,4), (2,4), (3,4)\}$
D$A \times B \times C$
Answer & Solution
Correct answer: C. $\{(1,4), (2,4), (3,4)\}$
$B \cap C = \{4\}$. So $A \times (B \cap C) = A \times \{4\} = \{(1,4), (2,4), (3,4)\}$.
This equals $(A \times B) \cap (A \times C)$ — illustrating the distributive law.
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