WBJEE · Maths · Sets and Relations
Let \(A, B, C\) are subsets of set \(X\). Then consider the validity of the following set theoretic statement :
- A \(A \cup(B \backslash C)=(A \cup B) \backslash(A \cup C)\)
- B \((A \backslash B) \backslash C=A \backslash(B \cup C)\)
- C \((A \cup B) \backslash A=A \backslash B\)
- D \(A \backslash C=B \backslash C\)
Answer & Solution
Correct Answer
(B) \((A \backslash B) \backslash C=A \backslash(B \cup C)\)
Step-by-step Solution
Detailed explanation
Hint: \(\begin{aligned} :(A \backslash B) \backslash C & =\left(A \cap B^{\prime}\right) \cap C^{\prime} \\ & =A \cap\left(B^{\prime} \cap C^{\prime}\right) \\ & =A \cap(B \cup C)^{\prime} \\ & =A \backslash(B \cup C) \end{aligned}\)
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