The value of the operation [9]+[8]∈ Z13 and to write the answer in the form [r] with 0≤r&lt;m.

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High School
Geometry
High school geometry
Congruence

vestirme4

Answered question

2021-03-22

The value of the operation $[9] + [8] \in$ $Z_{13}$ and to write the answer in the form [r] with $0 \leq r < m$ .

Answer & Explanation

lamanocornudaW

Skilled2021-03-24Added 85 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.
$[9] + [8] = [9 + 8] = [17]$
Since $17 \equiv 4 \pm o d 13$ . Thus $[9] + [8] = [4] \in$ $Z_{13}$ .
Therefore, the value of the expression is [4].

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