Answer by citadel for Show that each composite function $f_i \circ f_j$ is...
In cycle notation:\begin{alignat}{1}&f_1=(23)\\&f_2=(13)\\&f_3=(12)\\&f_4=(123)\\&f_5=(132)\\\end{alignat}By "completing a table etc." they mean to explicty prove that:$$\forall...
View ArticleAnswer by egreg for Show that each composite function $f_i \circ f_j$ is one...
If $f_0=\{(1,1),(2,2),(3,3)\}$ is the identity map, the six maps $\{f_0,f_1,f_2,f_3,f_4,f_5\}$ are six bijective maps $A\to A$.Since $|A|=3$, there are exactly $6=3!$ bijective maps $A\to A$, so the...
View ArticleShow that each composite function $f_i \circ f_j$ is one of the given functions
I'm just going through the problems that I got wrong on my discrete math exam, and I was not sure how to do this one. How would I go about making this chart? The chart has $f_1, \dots, f_5$ going...
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