The value of the operation [12]+[25] in Z7 and to write the answer in the...

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 $x=y(\mathrm{mod}m)$. 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.
[12] + [25] = [12 + 25] = [37]
Since $37\equiv 2(\mathrm{mod}7)$. Thus [12] + [25] = [2] in ${\displaystyle Z_7}$.
Therefore, the value of the expression is [2].