Question

To find the lexicographic ordering of the given \(n\) - tuples.

Short answer

The lexicographic ordering of the given \(n - \) tuples is \( \Rightarrow (1,0,1,0,1) > (0,1,1,1,0)\).

Step-by-step solution

Given data

Given data is \((1,0,1,0,1),(0,1,1,1,0)\).

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

Let us assume \(\left( {{a_1},{a_2},{a_3},{a_4},{a_5}} \right) = (1,0,1,0,1)\) And

\(\left( {{b_1},{b_2},{b_3}} \right) = (0,1,1,1,0) \in N \times N \times N \times N \times N\)

Which is less than or equal to lexicographic ordering

By observing \({a_1} > {b_1}\)

\((1,0,1,0,1) > (0,1,1,1,0)\).