Question: Practice Question 1 (will be discussed next class) Let be an asymmetric binary relation on a finite set X that does not have a cycle,

Practice Question 1 (will be discussed next class)

Let be an asymmetric binary relation on a finite set X that does not have a

cycle, that is there is no finite sequence of elements x1, x2, ... , xK, where K > 2,

such that x1 x2 ... xK x1.

Show (by induction on the size of X) that can be extended to a complete ordering (i.e., a complete, asymmetric, and transitive binary relation).

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