If A, B and C are three sets such that A cap | vedclass

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(B) Given: $A \cap B = A \cap C$ and $A \cup B = A \cup C$.Consider the set $B$. We can write $B = B \cap (A \cup B)$.Since $A \cup B = A \cup C$,we h

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$B = C$

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(B) Given: $A \cap B = A \cap C$ and $A \cup B = A \cup C$.Consider the set $B$. We can write $B = B \cap (A \cup B)$.Since $A \cup B = A \cup C$,we have $B = B \cap (A \cup C)$.Using the distributive law,$B = (B \cap A) \cup (B \cap C)$.Since $A \cap B = A \cap C$,we have $B = (A \cap C) \cup (B \cap C)$.By the distributive law,$B = (A \cup B) \cap C$.Since $A \cup B = A \cup C$,we have $B = (A \cup C) \cap C$.Since $(A \cup C) \cap C = C$,it follows that $B = C$.

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

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