120+10(9)≡ 0 (mod 11)
You asked:
Evaluate the congruence relation statement $10 \cdot 9 + 120 \equiv 0 \pmod{11}$.
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: $10 \cdot 9 + 120 \equiv 0 \pmod{11} \mapsto 210 \equiv 0 \pmod{11}$
$210 - 0 = 210$, which is not a multiple of $11$, so the congruence relation statement is not true.
This is because dividing $210$ by $11$ produces $19$ with a non-zero remainder of $1$.