If A, B and C are three sets such that A ? B = A ? C and A ? B = A ? C, then

Question

If A, B and C are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then

Smart Achievers · Accepted Answer

(2)

$Let x \in C and x \in A \Rightarrow x \in A \cap C$

$\Rightarrow x \in A \cap B . Thus x \in B$ $(∵ A \cap C = A \cap B)$

$Again suppose x \in C and x \notin A \Rightarrow x \in C \cup A$

$\Rightarrow x \in B \cup A \Rightarrow x \in B$

$Thus in both cases x \in C \Rightarrow x \in B$

$Hence C \subseteq B$ ...(1)

$Similarly we can show that B \subseteq C$ ...(2)

$Combining (1) and (2), we get B = C$

Want Us to Email you About Special Offers & Updates?