Here we need to just find one counter example that contradicts the validity of the given statement.

Suppose we set values a=0, b=1, c=3, m=4 in \(ac\equiv bc\pmod{m}\)

We get,

\(0\times 1\equiv 1\times 3\pmod 3\)

\(0=3\pmod 3\)

0=0

Thus, this congruence is satisfied.

Next let us plug these values in \(a\equiv b\pmod m\)

We get,

\(0\equiv 1\pmod 3\), which is obviously incorrect.

Thus a counterexample could be the set of value

a=0, b=1, c=3, m=4