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(A ⋂ B) ⋃ (¬A ⋂ D) ⋃ (B ⋂ D) = (A ⋂ B) ⋃ (¬A ⋂ D)

Answer 1

$(A \cap B) \cup (\neg A \cap D) \cup (B \cap D)\Leftrightarrow \cap B) \cup ((\neg A \cap D) \cup (B \cap D))\Leftrightarrow \\\Leftrightarrow (A \cap B) \cup ((B \cap D) \cup (\neg A \cap D))\Leftrightarrow (A \cap B) \cup (B \cap D) \cup (\neg A \cap D)\Leftrightarrow \\\Leftrightarrow (A \cap B) \cup (B \cap D) \cup (D \cap \neg A)\Leftrightarrow (A \cap B) \cup ((B \cap D) \cup (D \cap \neg A))\Leftrightarrow$$\Leftrightarrow (A \cap B) \cup (B \cap D) \cup (D \cap \neg A)\Leftrightarrow (A \cap B) \cup (D \cap B) \cup (D \cap \neg A)\Leftrightarrow \\\Leftrightarrow (A \cap B) \cup (B \cap D) \cup (\neg A \cap D)$