Art of Computer Programming problem

I'm not asking for the solution to this problem. It's just that I
don't understand what it means:

"Let S be well-ordered by <<, and for n>0 let Tn be the set of all n-
tuples (x1, x2, ..., xn) of elements xj in S. Define (x1, x2, ..., xn)
<<(y1, y2, ..., yn), if there is some k, 1<=k<=n, such that xj=yj for
1<=j<k, but xk<<yk in S. Is << a well-ordering of Tn?"

Note that by << a denote a symbol used in the book, which refers to
some relation on the set S. Describing the exact properties of << is
part of the problem, as you can see above.

It looks to me as a very badly-worded problem, but I'm probably wrong.
Any help appreciated.
.

Relevant Pages

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