Giải thích các bước giải:
$\begin{array}{l}
1)x \in A \cap \left( {B\backslash C} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
x \in A\\
x \in B\backslash C
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \in A\\
x \in B\\
x \notin C
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \in A \cap B\\
x \notin C
\end{array} \right.\\
\Leftrightarrow x \in \left( {A \cap B} \right)\backslash C\\
\Rightarrow A \cap \left( {B\backslash C} \right) = \left( {A \cap B} \right)\backslash C\\
2)x \in A\backslash \left( {B \cap C} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
x \in A\\
x \notin B \cap C
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \in A\\
\left[ \begin{array}{l}
x \notin B\\
x \notin C
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x \in A;x \notin B\\
x \in A;x \notin C
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x \in A\backslash B\\
x \in A\backslash C
\end{array} \right.\\
\Leftrightarrow x \in \left( {A\backslash B} \right) \cup \left( {A\backslash C} \right)\\
\Rightarrow A\backslash \left( {B \cap C} \right) = \left( {A\backslash B} \right) \cup \left( {A\backslash C} \right)
\end{array}$
Ta có đpcm.
