Lexicographical ordering - DISCRETE STRUCTURES

Question 1 UGC NET June-2020
Find the lexicographic ordering of the bit strings given below based on the ordering 0 < 1.
A) 001
B) 010
C) 011
D) 0001
E) 0101
Choose the correct answer from the options given below:

A – 001<010<011<0001<0101

B – 0001<001<010<0101<011

C – 0001<0101<001<010<011

D – 001<010<0001<0101<011

Show Answer With Best Explanation

Answer: b
Explanation:
Lexicographically means sorting in natural order, dictionary order.
The lexicographic order of the given bit strings will be:
0001<001<010<0101<011
Take 0001 & 001 for comparing. Compare each bit of 1st string with the corresponding bit of 2nd string.

It is clear that 0001< 001.