UPSKILL MATH PLUS

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Verify \(A \cap (B \cup C) = (A \cap B) \cup (A \cap C)\) using Venn diagrams.
 
Proof:
 
\(B \cup C =\)
 
\(A \cap (B \cup C) =\)
 ---- (\(1\))
 
\(A \cap B =\)
 
\(A \cap C =\)
 
\((A \cap B) \cup (A \cap C) =\)
 ---- (\(2\))
 
From equations (\(1\)) and (\(2\)), we have \(A \cap (B \cup C) = (A \cap B) \cup (A \cap C)\).
 
Hence, we proved.