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Let \(A, B, C\) are subsets of set \(X\). Then consider the validity of the following set theoretic statement :
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Verified Answer
The correct answer is:
\((A \backslash B) \backslash C=A \backslash(B \cup C)\)
Hint:
\(\begin{aligned}
:(A \backslash B) \backslash C & =\left(A \cap B^{\prime}\right) \cap C^{\prime} \\
& =A \cap\left(B^{\prime} \cap C^{\prime}\right) \\
& =A \cap(B \cup C)^{\prime} \\
& =A \backslash(B \cup C)
\end{aligned}\)
\(\begin{aligned}
:(A \backslash B) \backslash C & =\left(A \cap B^{\prime}\right) \cap C^{\prime} \\
& =A \cap\left(B^{\prime} \cap C^{\prime}\right) \\
& =A \cap(B \cup C)^{\prime} \\
& =A \backslash(B \cup C)
\end{aligned}\)
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