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.
- $$\text { If } a \equiv b ( \bmod m ) \text { and } c \equiv d ( \bmod m ) \text {, then } a c \equiv b + d ( \bmod m )$$