Question:
Using properties of sets show that
(i) $A \cup(A \cap B)=A$ (ii) $A \cap(A \cup B)=A$.
Solution:
(i) To show: $A \cup(A \cap B)=A$
We know that
$A \subset A$
$A \cap B \subset A$
$\therefore A \cup(A \cap B) \subset A \ldots(1)$
Also, $A \subset A \cup(A \cap B) \ldots$ (2)
$\therefore$ From $(1)$ and $(2), A \cup(A \cap B)=A$
(ii) To show: $A \cap(A \cup B)=A$
$A \cap(A \cup B)=(A \cap A) \cup(A \cap B)$
$=A \cup(A \cap B)$
$=A\{$ from $(1)\}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.