Let A be a finite set of size n. The number of elements in the power set of A x A is:
A. 2^n
B. 2^(n^2)
C. (2^n)^2
D. (2...

Question

Let A be a finite set of size n. The number of elements in the power set of A x A is:
A. 2^n
B. 2^(n^2)
C. (2^n)^2
D. (2^2)^n
E. None of the above

Accepted Answer

B. 2^(n^2) The Cartesian product A x A has n^2 ordered pairs. The power set of any set with m elements contains 2^m subsets. So |P(A x A)| = 2^(n^2). Note that 2^(n^2) and (2^n)^2 = 2^(2n) are different — n^2 grows much faster than 2n.

Let A be a finite set of size n. The number of elements in the power set of A x A is: A. 2^n B. 2^(n^2) C. (2^n)^2 D. (2^2)^n E. None of the above