Question

The value of the operation [43]+[31] in Z_{22} and to write the answer in the form [r] with 0\leq r < m.

Congruence
ANSWERED
asked 2021-05-08
The value of the operation [43]+[31] in \(\displaystyle{Z}_{{{22}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\)</span>.

Answers (1)

2021-05-10
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.
[43] + [31] = [43 + 31] = [74]
Since \(\displaystyle{74}={8}\pm{o}{d}{22}\). Thus [43] + [31] = [8] in \(\displaystyle{Z}_{{{22}}}\).
Therefore, the value of the expression is [8].
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