Question

The value of the operation [16]+[9] in Z_{6} and to write the answer in the form [r] with 0\leq r<m.

Congruence
ANSWERED
asked 2021-04-17

The value of the operation [16]+[9] in \(\displaystyle{Z}_{{{6}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).

Expert Answers (1)

2021-04-19
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.
[16] + [9] = [16 + 9] = [25]
Since \(\displaystyle{25}\equiv{1}\pm{o}{d}{6}\). Thus [16] + [9] = [1] in \(\displaystyle{Z}_{{{6}}}\).
Therefore, the value of the expression is [1].
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