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

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(C) We know that for any two sets $A$ and $B$,the union $A \cup B$ contains all elements that are in $A$ or in $B$,while the intersection $A \cap B$ c

Vedclass · Accepted Answer

$A = B$

Vedclass · Answer

(C) We know that for any two sets $A$ and $B$,the union $A \cup B$ contains all elements that are in $A$ or in $B$,while the intersection $A \cap B$ contains only elements that are in both $A$ and $B$.It is a fundamental property that $A \cap B \subseteq A \subseteq A \cup B$ and $A \cap B \subseteq B \subseteq A \cup B$.If $A \cup B = A \cap B$,then all these sets must be equal.Specifically,$A \subseteq A \cup B$ and $A \cup B = A \cap B$ implies $A \subseteq A \cap B$.Since $A \cap B \subseteq A$ is always true,$A \subseteq A \cap B$ and $A \cap B \subseteq A$ together imply $A = A \cap B$,which means $A \subseteq B$.Similarly,$B \subseteq A \cup B$ and $A \cup B = A \cap B$ implies $B \subseteq A \cap B$,which means $B \subseteq A$.Since $A \subseteq B$ and $B \subseteq A$,it follows 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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