Question: Question: Let A be a set with |A| = n for some positive integer n, and relation R defined on A, (a)how many possible R

Question:Let A be a set with |A| = n for some positive integer n, and relation R defined on A,

  1. (a)how many possible R are there ? (hint: R is a well defined relation on A if and only if R A A).

Answer: 2n2

Let S = {(x,y) | x A and y A}, any subset of S is a relation on A, and there are 2n2 subsets of S.

why is the answer 2^(n^2)? I do not understand this.

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