Question

The value of the operation [8][7] in Z_{6} and to write the answer in the form [r] with 0\leq r < m.

Congruence
ANSWERED
asked 2021-04-26
The value of the operation [8][7] in \(\displaystyle{Z}_{{{6}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\)</span>.

Answers (1)

2021-04-28
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.
\(\displaystyle{\left[{8}\right]}{\left[{7}\right]}={\left[{8}\times{7}\right]}\)
=[56]
Since \(\displaystyle{56}\equiv{2}\pm{o}{d}{6}\). Thus [8][7]=[2] in \(\displaystyle{Z}_{{{6}}}\).
Therefore, the value of the expression is [2].
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