Question

$Z$ is the set of integers and $N$ is the set of natural numbers. If $b\in Z,c\in Z$ and $n\in N,$ if $b$ and $c$ are said to be congruent with respect to modulo $n,$ then symbolically it is written as $b\equiv c\left(modn\right)$.

Which of the following is true

• A. $4\equiv 7\left(mod5\right)$
• B. $118\equiv 18\left(mod5\right)$
• C. $110\equiv 93\left(mod12\right)$
• D. $63\equiv 9\left(mod11\right)$

Answer 1

The correct option is B $118\equiv 18\left(mod5\right)$

In computing, the modulo operation finds the remainder after division of one number by another

118 on division by 5 will give 3 as remainder

18 will give 3 as remainder on division by 5

So 118 and 18 are congruent with respect to modulo 5