Use Venn Diagrams to Determine Which of the Following Identities $( B \cup D ) \cap G = ( B \cup D ) \cap G$

question 67

Multiple Choice

Use Venn Diagrams to determine which of the following identities are true for the subsets B, D, and G of T.

• A) \(( B \cup D ) \cap G = ( B \cup D ) \cap G\) (Associative Law), and \(B \cup ( D \cap G ) = ( B \cap G ) \cup ( D \cap G )\) (Distributive law)
• B) \(( B \cup D ) ^ { \prime } = B ^ { \prime } \cap G ^ { \prime }\) (De Morgan's law), and \(( B \cap D ) \cap G = B \cap ( D \cap G )\) (Associative Law)
• C) \(( B \cap D ) ^ { \prime } = B ^ { \prime } \cup D ^ { \prime }\) (De Morgan's law), and \(( B \cup D ) \cup T = B \cup ( D \cup T )\) (Associative Law)
• D) \(( B \cap D ) ^ { \prime } = B ^ { \prime } \cap D ^ { \prime }\) (De Morgan's law), and \(B \cup ( D \cap T ) = ( B \cap T ) \cup ( B \cap T )\) (Distributive law)
• E) \(B \cup ( D \cap G ) = ( B \cap G ) \cup ( B \cap G )\) (Distributive law), and \(( B \cap D ) ^ { \prime } = B ^ { \prime } \cup D ^ { \prime }\) (De Morgan's law)

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