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 :

Accepted Answer

From the given conditions, we have :

A \cap  B = A \cap  C : The intersection of set A with set B is the same as the intersection of set A with set C. This indicates that all elements common to A and B are also common to A and C, and vice versa.

A \cup  B = A \cup  C : The union of set A with set B is the same as the union of set A with set C. This indicates that all elements in A, B, and C are the same.

From these two conditions, we can infer that set B is equal to set C because every element of B is also an element of C and vice versa. Hence, Option B : B = C is the correct answer.

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