Determine Whether Each of the Following "Theorems" Is True or False

True/False

determine whether each of the following "theorems" is true or false. Assume that a, b, c, d,
and m are integers with m > 1.
- $$\text { If } a \equiv b ( \bmod m ) , \text { then } 2 a \equiv 2 b ( \bmod 2 m )$$