I have read this question in an exercise book:
"Consider the following strict ordering (denoted by >)...
a > b > c > d
Now consider in what way the following triples are related in >^3
(c, d, a),(d, a, d),(d, d, d),(a, a, a),(d, c, d)."
I am unsure what exactly the question is asking. Is it perhaps asking what properties of relation it has? e.g reflexive, irreflexive, total, linear, transitive etc. Any help would be great.
If I’m interpreting the question correctly, it misuses the expression $>^3$ to mean the relation on $\{a,b,c,d\}^3$ defined by setting $\langle u,v,w\rangle>^3\langle x,y,z\rangle$ if and only if $u>x$, $v>y$, and $w>z$. Thus, for instance, $\langle a,a,a\rangle>^3\langle d,d,d\rangle$, because $a>d$, but $\langle c,d,a\rangle\not>^3\langle d,d,d\rangle$, because even though $c>d$ and $a>d$, in the middle $d\not>d$. It appears that for each pair of the listed triples you are to determine which member of the pair (if either) is $>^3$ the other.