Solution:

(i) We need to show: $A \cup(A \cap B)=A$

As it is known that,

$\begin{array}{l}
A \subset A \\
A \cap B \subset A \\
\therefore A \cup(A \cap B) \subset A……….(i)
\end{array}$

Also, as per the question,

We have:

$A \subset A \cup(A \cap B)$………….(ii)

As a result, from eq. (i) and (ii)

We have:

$A \cup(A \cap B)=A$

(ii) We need to show,

$\begin{array}{l}
A \cap(A \cup B)=A \\
A \cap(A \cup B)=(A \cap A) \cup(A \cap B) \\
=A \cup(A \cap B) \\
=A
\end{array}$