120+10(8)≡ 0 (mod 11)
You asked:
Evaluate the congruence relation statement $10 \cdot 8 + 120 \equiv 0 \pmod{11}$.
MathBot Answer:
This congruence relation statement is not true.
Two expressions $a$ and $b$ are congruent modulo $n$ if $a - b$ is a multiple of $n$.
Evaluating both sides: $10 \cdot 8 + 120 \equiv 0 \pmod{11} \mapsto 200 \equiv 0 \pmod{11}$
$200 - 0 = 200$, which is not a multiple of $11$, so the congruence relation statement is not true.
This is because dividing $200$ by $11$ produces $18$ with a non-zero remainder of $2$.