Monday, 21 December 2015

discrete mathematics - Number of bijective functions (two finite sets)


Let M and N be finite sets, with |M|=m and |N|=n.



a)Find out the number of bijective functions f:MN. Look at the cases: mn and m=n.





Bijective: Every element in N has exactly one partner in M.



mn: That means either m<n or m>n.



If m>n then wouldn't every element in N have exactly one partner in M?



If $m then it wouldn't work, since some elements in N wouldn't have a partner in M.



m=n: Here every element in N will have exactly one partner in M.




So you can get a bijective functions if m>n or m=n.



For m=n number of bijective functions would be: m



For m>n number of bijective functions would be: n



I'm not too sure on my answer.

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