Let S be the set of all strings in a$\text{'}$s and b$\text{'}$s$,$ and define

C: S $->$ S

by

C$($s$)=$ as$,$

for each

s in S$.$

$($C is called concatenation by a on the left.$)$

$($a$)$

Is C one$-$to$-$one?

To answer this question, suppose

s$1$

and

s$2$

are strings in S such that

C$($s$1)=$ C$($s$2).$

Use the definition of C to write this equation in terms of a$,$

s$1,$

and

s$2$

as follows.