Question

The value of the operation [8]+[6] in Z_{12} and to write the answer in the form [r] with 0\leq r < m.

Transformation properties
ANSWERED
asked 2021-03-10

The value of the operation [8]+[6] in \(\displaystyle{Z}_{{{12}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).

Expert Answers (1)

2021-03-12
Definition used:
Congruence.
Let m be an integer greater than 1. If x and y are integers, then x is congruent to y modulo m if x — y is divisible by m. It can be represented as \(\displaystyle{x}={y}\pm{o}{d}{m}\). This relation is called as congruence modulo m.
Calculation:
It is known that, [x] + [y] = [x+y].
Then, the value of the expression becomes as follows.
[8] + [6] = [8 + 6] = [14]
Since \(\displaystyle{14}\equiv{2}\pm{o}{d}{12}\). Thus [8] + [6] = [2] in \(\displaystyle{Z}_{{{12}}}\).
Therefore, the value of the expression is [2].
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