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How many one-to-one correspondences exist between two sets with A) 8 elements each? B) n-1 elements each?Asked by Stacey
How many one-to-one correspondences exist between two sets with
A) 8 elements each?
B) n-1 elements each?
A) 8 elements each?
B) n-1 elements each?
Answers
Answered by
David
Do you mean how many separate pairings exist between two groups of objects, each of which contains eight elements? If so, the answer is (8 x 8) = 64.
The reason I'm slightly cautious about the answer is that I'd have expected the second part of the question to be asking the same about n elements each as opposed to (n-1), unless this is leading up to a simple demonstration of mathematical induction, i.e. demonstrate the answer for n=1, then prove that if it's true for (n-1) then it must be true for n.
The reason I'm slightly cautious about the answer is that I'd have expected the second part of the question to be asking the same about n elements each as opposed to (n-1), unless this is leading up to a simple demonstration of mathematical induction, i.e. demonstrate the answer for n=1, then prove that if it's true for (n-1) then it must be true for n.
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