1. is right.I have no idea how to solve this. Any advice? View attachment 32528
@Loki123 Can you tell us how many functions [imath]f:\{a,b,c,d\}\to\{a,b,c,d\}[/imath] are there?I have no idea how to solve this. Any advice? View attachment 32528
You can also figure out the total number of constant functions.@Loki123 Can you tell us how many functions [imath]f:\{a,b,c,d\}\to\{a,b,c,d\}[/imath] are there?
How many of those are injections? Is every one of those injections a bijection?
Please answer.
i am having difficulty understanding how to show functions using permutations, combinations or variations@Loki123 Can you tell us how many functions [imath]f:\{a,b,c,d\}\to\{a,b,c,d\}[/imath] are there?
How many of those are injections? Is every one of those injections a bijection?
Please answer.
The reason you are having trouble is simply because those are not the way to do this question.i am having difficulty understanding how to show functions using permutations, combinations or variations
YES! Thank you sooo much!The reason you are having trouble is simply because those are not the way to do this question.
If [imath]A[/imath] is a set then [imath]|A|[/imath] is the number members in the set.
The number of functions [imath]f:A\to B[/imath] is [imath]|B|^{|A|}[/imath] If [imath]A=\{a,b,c,d[/imath]
The number of functions [imath]f:A\to A[/imath] is [imath]4^{4}=256[/imath].
The number of injections [imath]f:A\to A[/imath] is [imath]4!=24[/imath]. In this case every injection is a surjection.
The number of constant functions [imath]f:A\to A[/imath] is [imath]4[/imath]. The image set is only one term.
Do you see there are no permutations, combinations or variations to it?
Tectonically it is that the finial set is only one term. Every element of the set is mapped to the same term.YES! Thank you sooo much!
just one question, I don't understand what a constant function would represent here.
So a, b, c, d would all be mapped into a, then b, then c, then d. Got it.Tectonically it is that the finial set is only one term. Every element of the set is mapped to the same term.
thank you!Looks good to me.