Thank you for reporting, we will resolve it shortly
Q.
The relation of "congruence modulo" is :
Relations and Functions - Part 2
Solution:
Congruence modulo: An integer ‘a’ is said to be congruent to another integer ‘b’
module ‘m’ if a - b is divisible by m and expressed as: a $\equiv$ b (mod m)
The integer m is called the modulus of the congruence.
Now suppose a, b, c $\in$ I (congruence of modulo)
Let a $\equiv$ b (mod m)
Since a $\equiv$ a (mod m) and o $\doteq$ m
so the function is Reflexive.
Now if a $\equiv$ b (mod m) then
Also b $\equiv$ a (mod m) because (a - b) divides by m, then b - a also divides by m. Thus function is symmetric.
Now If a $\equiv$ b (mod m) and b $\equiv$ c (mod m)
$\Rightarrow \, \frac{a-b}{m}$ and $\frac{b -c}{m} ;$ So $\frac{a-c}{m}$
$\therefore \, a \equiv c $ (mod m) thus function is Transitive.
Thus the relation is Equivalence Relation.