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Question Number 115418 by mohammad17 last updated on 25/Sep/20

Commented by mohammad17 last updated on 25/Sep/20

$h e l p m e s i r i w a n t (H . W)$
	Answered by Dwaipayan Shikari last updated on 25/Sep/20

	$For any Set$ $A \cap \emptyset = A$ $A \cap A = A$ $Suppose x \in A$ $So x \in A \cap A$ $And A \cap A = A$ $A \cap C = C \cap A$ $Suppose x \in A and x \in C$ $x \in A \cap C$ $x \in C \cap A$ $So C \cap A = A \cap C$
	Answered by Dwaipayan Shikari last updated on 25/Sep/20

	$x is an element of set A (x \in A)$ $And (x \in B)$ $And x \in (A \cap B) (By definition)$ $And (A \cap B) \subseteq A$ $Also (A \cap B) \subseteq B$
	Commented by mohammad17 last updated on 25/Sep/20

	$y e s s i r i w a n t o t h e r q u e s t i o n i n s a m e t h i s m e t h o d$
	Commented by Dwaipayan Shikari last updated on 25/Sep/20

	$It is better to use Venn diagram in Q 7$
	Answered by MWSuSon last updated on 25/Sep/20

	$by using the definition of set equality$ $and logical equivalence$ $X = Y iff \forall x \in U, (x \in X \Leftrightarrow x \in Y) we can$ $show 6 and 7 .$ $6) let x \in (A \cap (B \cup C)) \Leftrightarrow x \in A \land x \in (B \cup C)$ $\Leftrightarrow x \in A \land (x \in B \lor x \in C)$ $\Leftrightarrow (x \in A \land x \in B) \lor (x \in A \land x \in C)$ $\Leftrightarrow x \in (A \cap B) \cup (A \cap C)$ $therefore A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$ $same way for 7$
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