If A and B are two sets,then A cup B = A cap | vedclass

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Question

(C) Given $A \cup B = A \cap B$.Let $x \in A$. Since $A \subseteq A \cup B$,we have $x \in A \cup B$.Since $A \cup B = A \cap B$,it follows that $x \i

Vedclass · Accepted Answer

$A = B$

Vedclass · Answer

(C) Given $A \cup B = A \cap B$.Let $x \in A$. Since $A \subseteq A \cup B$,we have $x \in A \cup B$.Since $A \cup B = A \cap B$,it follows that $x \in A \cap B$.By definition of intersection,$x \in A \cap B \Rightarrow x \in A$ and $x \in B$. Thus,$x \in B$.Therefore,$A \subseteq B$.Similarly,let $x \in B$. Since $B \subseteq A \cup B$,we have $x \in A \cup B$.Since $A \cup B = A \cap B$,it follows that $x \in A \cap B$.By definition of intersection,$x \in A \cap B \Rightarrow x \in A$ and $x \in B$. Thus,$x \in A$.Therefore,$B \subseteq A$.Since $A \subseteq B$ and $B \subseteq A$,we conclude that $A = B$.

If $A$ and $B$ are two sets,then $A \cup B = A \cap B$ if and only if

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