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Number of Elements in a Cartesian Product

If A = 1, 2, ...

Question

If $A = {1, 2, 3, 4, 5, 6},$ $B = {2, 4, 6, 8, 10, 12}$ $C = {6, 12, 18, 24, 30, 36},$ $D = {4, 16, 64},$ then $n ((A \times B) \cap (C \times D))$ is

A

1

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B

0

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C

8

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D

6

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Solution

The correct option is A $1$
$(A \times B) \cap (C \times D) = (A \cap C) \times (B \cap D) = {6} \times {4} = {(6, 4)}$

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Number of Elements in a Cartesian Product

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