1. ## Help with Sets

Please tell me that the following statement is true or false :

(AÈB) Ç (AÇB¢) = A

I think it should be
(AÈB) Ç (AÇB¢) = A - B

2. Hello, goodone!

Is the following statement is true or false?

$(A \cup B) \cap (A \cap B')$

I think it should be: . $A - B$ . . . . Right!
I'll let you supply the reasons . . .

. . $\begin{array}{cccc}
(A \cup B) \cap A \cap B' \\ \\
(A\cup B) \cap B' \cap A \\ \\
\bigg[(A \cap B') \cup (B \cap B')\bigg] \cap A \\ \\
\bigg[(A \cap B') \cup \emptyset\bigg] \cap A \\ \\
(A \cap B') \cap A \end{array}$

. . . . . $\begin{array}{cc}A \cap (B' \cap A) \\ \\
A \cap (A \cap B') \\ \\
(A \cap A) \cap B' \\ \\
A \cap B' \\ \\
A - B
\end{array}$