For any three sets A, B and C
(a) \(A\cap(B-C)=(A\cap B)-(A\cap C)\)
(b) \(A\cap(B-C)=(A\cap B)-C\)
(c) \(A\cup(B-C)=(A\cup B)\cap(A\cup C’)\)
(d) \(A\cup(B-C)=(A\cup B)-(A\cup C)\)
Solution
\[ B-C=B\cap C’ \]
Therefore,
\[ A\cap(B-C) \]
\[ =A\cap(B\cap C’) \]
\[ =(A\cap B)\cap C’ \]
\[ =(A\cap B)-C \]
Hence, option (b) is correct.
Answer
\[ \boxed{A\cap(B-C)=(A\cap B)-C} \]
Correct option: (b)