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Question

If two sets have 720 one-to-one correspondences pairing them, how many elements are in each set?
There are 720 one-to-one correspondences between two sets with
nothing elements each.

Answer 1

Two sets can only have a one-to-one correspondence if they have the same cardinality; that is, there are exactly the same number of items in each set.  So if each item in set A corresponds to exactly one item in set B and there are exactly 720 correspondences, then each set has exactly 720 items in it.

 

Example:

     A = {1, 2, 3}

     B = {a, b, c}

 

     Correspondences:

     1 → a

     2 → b

     3 → c

 

     Three correspondences, three members in each set.