Answer:
The given congruence is false.
Step-by-step explanation:
Given : Expression [tex]12 \equiv 10 \mod 5[/tex]
To find : Determine whether the congruence is true or false ?
Solution :
The congruence is in the form [tex]x\mod y\equiv r[/tex]
where, x is the dividend
y is divisor
r is the remainder
So, We find [tex]10 \mod 5[/tex]
We know, 10 is completely divide by 5 and we get quotient is 2 and remainder is 0.
[tex]10 \mod 5=0[/tex]
As [tex]0\neq 12[/tex]
Therefore, The given congruence is false.
