Let A = {x : x is a square of a natural number and x is less than 100} and B is a set of even natural numbers. What is the cardinality of $A \cap B$ ?

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None of the above

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Solution

The correct option is B 4
$A = {1, 4. 9. 16, 25, 36, 49, 64, 81}$
$B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 24, 26, 28, 30, 32, 34, 36, 38, . . .}$
$A \cap B = {4, 16, 36, 64}$
Hence, $n (a \cap B) = 4$ .

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