Question

The value of the expression [9]+[11] in \(\displaystyle{Z}_{{{15}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).

Answer 1

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.
[9] + [11] = [9 + 11] = [20]
Since \(\displaystyle{20}\equiv{5}\pm{o}{d}{15}\). Thus [9] + [11] = [5] in \(\displaystyle{Z}_{{{15}}}\).
Therefore, the value of the expression is [5].