Addition Modulo

Now we are going to discuss a new type of addition which is known as “addition modulo m” and written in the form  where a and b belongs to an integer and m is any fixed positive integer.

• The identity element of a group is always unique.
• The inverse of each element of a group is unique, i.e., in a group G with operation * for every, there is only element such that, e being the identity.

• Closure Axiom : If all the elements of the table belong to the set G (say) then G is closed under the Composition a (say). If any of the elements of the table does not belong to the set, the set is not closed.