Question

The value of the operation [12]+[25] in Z_{7} and to write the answer in the form [r] with 0\leq r<m.

Congruence
ANSWERED
asked 2021-04-04

The value of the operation [12]+[25] in \(\displaystyle{Z}_{{{7}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).

Answers (1)

2021-04-06

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 \(x = y \pmod m\). 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.
[12] + [25] = [12 + 25] = [37]
Since \(37 \equiv 2 \pmod 7\). Thus [12] + [25] = [2] in \(\displaystyle{Z}_{{{7}}}\).
Therefore, the value of the expression is [2].

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