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27 votes

Let A be a finite set of size n. The number of elements in the power set of $A\times A$ is:

  1. $2^{2^n}$
  2. $2^{n^2}$
  3. $\left(2^n\right)^2$
  4. $\left(2^2\right)^n$
  5. None of the above
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3 Answers

Best answer
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41 votes
Cardinality of $A\times A = n^2$
Cardinality of power  set of $A\times A = 2^{n^2}$

Correct Answer: $B$
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14 votes
14 votes

$|A| = n$  ,  $ |p(A)| = 2^n$

$| A×A| =n^2$

$| p(A×A)|$ =$2^{n^{2}}$

Option (B) is the correct answer.

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