9. Five mark exercise problems IV

If \(A = \{x: x \in Z, -2 < x \leq 4\}\), \(B = \{x: x \in W, x \leq 5\}\), \(C = \{-4, -1, 0, 2, 3, 4\}\), then verify \(A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\).

 

Answer:

 

\(A =\) $\left\{i,i,i,i,i,i\right\}$

 

\(B =\) $\left\{i,i,i,i,i,i\right\}$

 

\(C = \{-4, -1, 0, 2, 3, 4\}\)

 

\(A \cup (B \cap C) =\) $\left\{i,i,i,i,i,i\right\}$

 

\(A \cup B =\) $\left\{i,i,i,i,i,i,i\right\}$

 

\(A \cup C =\) $\left\{i,i,i,i,i,i,i\right\}$

 

\((A \cup B) \cap (A \cup C) =\) $\left\{i,i,i,i,i,i\right\}$

 

Thus, \(A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\).

 

Hence, we proved.

 

(Note: Enter the numbers in ascending order.)