I"n this question we shall work with the lexicograpnic products of sequences of integers. The lexicographic product lex $(a,b)$ of two sequences $a,b$ may be defined as the sequence that looks like

$a[0]frownbfrowna[1]frownbdotsnota[n-1]frownb,$

if $a$ is a sequence of length $n$ and $$ is the sign for concatenation.

State what it would mean for lex to be $($i$)$ conmutative $($ii$)$ associative. Show by finding examples that lex is neither commutative nor associative.

Given the lengths of a and $b,$ what is the length of lex$(a,b)?$

Describe an algorithm to calculate lex$(a,b)$ for a and $b$ whose length is known in advance, and implement the algorithm in $C.$

Modify the program so that you are able to deal with lex $(a,b)$ for a and $b$ whose length is not known in advance. $"$ Explain to me how this qiestion is solved, in clear details with simplified explanation, so that in my upcoming modterm I would be able to do this question very well