# The value of the operation [5][12] in Z_{8} and to write the answer in the form [r] with 0\leq r<m.

Brittney Lord 2021-03-15 Answered

The value of the operation [5][12] in ${Z}_{8}$ and to write the answer in the form [r] with $0\le r.

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## Expert Answer

Yusuf Keller
Answered 2021-03-17 Author has 90 answers
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 $x=y±odm$. This relation is called as congruence modulo m.
Calculation:
It is known that, [x] [y] = [xy].
Then, the value of the expression becomes as follows.
$\left[5\right]\left[12\right]=\left[5×12\right]=\left[60\right]$
Since $60\equiv 4±od8$. Thus [5] [12] = [4] in ${Z}_{8}$.
Therefore, the value of the expression is [5].
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