Let +6 (addition modulo 6) be a binary operation on S = {0, 1, 2, 3, 4, 5}. Write the value of 2 +6 4–1 +6 3–1.

From the definition of addition modulo :-

a*b = (m is the base of the modulo)


Here the base is 6 and the set is S = {0,1,2,3,4,5}


So, we can make the composition table as :-


*



0



1



2



3



4



5



0



0



1



2



3



4



5



1



1



2



3



4



5



0



2



2



3



4



5



0



1



3



3



4



5



0



1



2



4



4



5



0



1



2



3



5



5



0



1



2



3



4



It is clear that 1 is the identity element of this binary operation.


The inverse of 4 is 3 while the inverse of 3 is 4.


∴ 2 4-1 3-1 = 2 3 4 = 3


1