Using that for any sets $\mathrm{A}$ and $\mathrm{B},$
$A \cup(A \cap B)=A$
Using that for any sets $\mathrm{A}$ and $\mathrm{B},$
$A \cup(A \cap B)=A$
To show: $A \cup(A \cap B)=A$
We know that
$A \subset A$
$A \cap B \subset A$
$\therefore A \cup(A \cap B) \subset A$ ..........$(1)$
Also, $A \subset A \cup(A \cap B)$ ..............$(2)$
$\therefore$ From $(1)$ and $(2), A \cup(A \cap B)=A$
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