Key to "The value of the operation [8]+[6] in Z12..."

High School
Geometry
High school geometry
Transformation properties

facas9

Answered question

2021-03-10

The value of the operation [8]+[6] in $Z_{12}$ and to write the answer in the form [r] with $0 \leq r < m$ .

Answer & Explanation

komunidadO

Skilled2021-03-12Added 86 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 \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.
[8] + [6] = [8 + 6] = [14]
Since

14 \equiv 2 \pm o d 12

. Thus [8] + [6] = [2] in

Z_{12}

.
Therefore, the value of the expression is [2].

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