# The value of the expression [9]+[11] in Z_{15} and to write the answer in the form [r] with 0\leq r < m.

The value of the expression [9]+[11] in ${Z}_{15}$ and to write the answer in the form [r] with $0\le r.

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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] = [x+y].
Then, the value of the expression becomes as follows.
[9] + [11] = [9 + 11] = [20]
Since $20\equiv 5±od15$. Thus [9] + [11] = [5] in ${Z}_{15}$.
Therefore, the value of the expression is [5].