Bài tập 1.44 trang 19 SBT Toán 10

a) Ta có : \(x \in \left( {A \cap B} \right) \cup A \Leftrightarrow \left[ \begin{array}{l}
x \in A \cap B\\
x \in A
\end{array} \right. \Leftrightarrow x \in A\)

Vậy (A∩B) ∪ A = A

b) Ta có \(x \in \left( {A \cup B} \right) \cap B \Leftrightarrow \left[ \begin{array}{l}
x \in A \cup B\\
x \in B
\end{array} \right. \Leftrightarrow x \in B\)

Vậy (A∪B) ∩ B = B

c) Ta có \(x \in \left( {A\backslash B} \right) \cup B \Leftrightarrow \left[ \begin{array}{l}
x \in A\backslash B\\
x \in B
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x \in A\\
x \notin B
\end{array} \right.\\
x \in B
\end{array} \right. \Leftrightarrow x \in A \cup B\)

Vậy (A∖B) ∪ B = A ∪ B

d) Ta có \(x \in \left( {A\backslash B} \right) \cap \left( {B\backslash A} \right) \Leftrightarrow \left\{ \begin{array}{l}
x \in A\backslash B\\
x \in B\backslash A
\end{array} \right. \Leftrightarrow x \in \emptyset \)

Vậy \(\left( {A\backslash B} \right) \cap \left( {B\backslash A} \right) = \emptyset \)

-- Mod Toán 10 HỌC247