
Asymmetric Relationships
Just for some fun. I am trying to put the following phrase in mathematical form; "asymmetry of the correlation among beauty, attraction, and sexuality". Correct me if I am wrong and it would be helpful if this can put in a simpler form.
$\displaystyle a = attraction$, $\displaystyle b = beauty$, $\displaystyle s = sexuality$
$\displaystyle c_{ab} = corr(a,b)$, $\displaystyle c_{bs} = corr(b,s)$, $\displaystyle c_{sa} = corr(s,a)$
$\displaystyle \exists c_{ab},c_{bs} \in X, c_{ab}Rc_{bs} \rightarrow \lnot(c_{bs}Rc_{ab})$
$\displaystyle \exists c_{bs},c_{sa} \in Y, c_{bs}Rc_{sa} \rightarrow \lnot(c_{sa}Rc_{bs})$
$\displaystyle \exists c_{sa},c_{ab} \in (X \cup Y), c_{sa}Rc_{ab} \rightarrow \lnot(c_{ab}Rc_{sa})$