UPSKILL MATH PLUS

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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:
 
\(A =\) i,i,i,i,i,i
 
\(B =\) i,i,i,i,i,i
 
\(C = \{-4, -1, 0, 2, 3, 4\}\)
 
\(A \cup (B \cap C) =\) i,i,i,i,i,i
 
\(A \cup B =\) i,i,i,i,i,i,i
 
\(A \cup C =\) i,i,i,i,i,i,i
 
\((A \cup B) \cap (A \cup C) =\) i,i,i,i,i,i
 
Thus, \(A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\).
 
Hence, we proved.
 
(Note: Enter the numbers in ascending order.)