i got confused by this question seems relatively simple but dnt get it.

how many non-injective functions are there from {1,2,3,4} to {1,2,3,4,5}? How many non-injective functions are there from {1,2,3,4,5} to {1,2,3,4}?

thanks.

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- May 31st 2008, 08:53 AMskystarinjective functions
i got confused by this question seems relatively simple but dnt get it.

how many non-injective functions are there from {1,2,3,4} to {1,2,3,4,5}? How many non-injective functions are there from {1,2,3,4,5} to {1,2,3,4}?

thanks. - May 31st 2008, 09:17 AMPlato
Using a usual notation for sets of functions $\displaystyle B^A = \left\{ {f|f:A \mapsto B} \right\} \Rightarrow \quad \left| {B^A } \right| = \left( {\left| B \right|} \right)^{\left| A \right|}$, then if $\displaystyle A = \left\{ {1,2,3,4} \right\}\,\& \,B = \left\{ {1,2,3,4,5} \right\}$ there are $\displaystyle 5^4$ functions from A to B. Of those $\displaystyle (5)(4)(3)(2)$ are injections. So how many non-injections are there?

There are no injections from B to A. WHY? - May 31st 2008, 09:28 AMskystar
because B has more elements than A

when you say (5)(4)(3)(2)..what do you mean.thanks - May 31st 2008, 09:32 AMPlato