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.

\(\displaystyle{\left[{8}\right]}{\left[{7}\right]}={\left[{8}\times{7}\right]}\)

=[56]

Since \(\displaystyle{56}\equiv{2}\pm{o}{d}{6}\). Thus [8][7]=[2] in \(\displaystyle{Z}_{{{6}}}\).

Therefore, the value of the expression is [2].