Explained: "The value of the expression [5]+[10] in Z11..."

High School
Geometry
High school geometry
Congruence

UkusakazaL

Answered question

2021-05-08

The value of the expression [5]+[10] in $Z_{11}$ and to write the answer in the form [r] with $0 \leq r < m$ .

Answer & Explanation

Nicole Conner

Skilled2021-05-10Added 97 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.
[5] + [10] = [5 + 10] = [15]
Since

15 \equiv 4 \pm o d 11

. Thus [5] + [10] = [4] in

Z_{11}

.
Therefore, the value of the expression is [4].

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