Solution:

Given

Now we have to verify

\[\left( A\text{ }+\text{ }B \right)\text{ }+\text{ }C\text{ }=\text{ }A\text{ }+\text{ }\left( B\text{ }+\text{ }C \right)\]

First consider

\[LHS,\text{ }\left( A\text{ }+\text{ }B \right)\text{ }+\text{ }C,\]

Now consider RHS, that is

\[A\text{ }+\text{ }\left( B\text{ }+\text{ }C \right)\]

Therefore

\[LHS\text{ }=\text{ }RHS\]

Hence

\[\left( A\text{ }+\text{ }B \right)\text{ }+\text{ }C\text{ }=\text{ }A\text{ }+\text{ }\left( B\text{ }+\text{ }C \right)\]