Question

To find the lexicographic ordering of the given strings of lower case English letters

Short answer

The lexicographic ordering of the given strings of lower case English letters \( quack<quacking\).

Step-by-step solution

Given data

Given data is zoo \(zoo,zero,zoom,zoo\log y,zoo\log ical\).

Concept used of lexicographic order

An ordering for the Cartesian product\( \times \)of any two sets\(A\)and\(B\)with order relations\( < A\)and\( < B\), respectively, such that if\(\left( {{a_1},{b_1}} \right)\)and\(\left( {{a_2},{b_2}} \right)\)both belong to\(A \times B\), then\(\left( {{a_1},{b_1}} \right) < \left( {{a_2},{b_2}} \right)\)iff either

1.\({a_1} < A{a_2}\), or

2.\({a_1} = {a_2}\)and\({b_1} < B{b_2}\).

Find the lexicographic order

Consider the given english lowercase letters \(zoo,zero,zoom,zoo\log y,zoo\log ical\)

\(zoo < zoo\log ical\)

\(zoological < zoology\)

\(zoology < zoom\)

Therefoe, \(zoo{\rm{ }} < {\rm{ }}zoological{\rm{ }} < zoology{\rm{ }} < zoom\).