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 are

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).
  2. (b)how many reflexive R are there ?
  3. (c)how many symmetric R are there ?

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