Let M and N be finite sets, with |M|=m and |N|=n.
a)Find out the number of bijective functions f:M→N. Look at the cases: m≠n and m=n.
Bijective: Every element in N has exactly one partner in M.
m≠n: 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
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.
No comments:
Post a Comment