Unformatted text preview: ˆ n [ k =1 A k ! = n [ k =1 ( B ∩ A k ) . 4. (a) (12 pts.) For all sets A , B , C , D , prove that ( A × B ) ∪ ( C × D ) ⊆ ( A ∪ C ) × ( B ∪ D ) . (b) (4 pts.) Find an example of sets A , B , C , and D where the inclusion in part (a) is proper, that is, where ( A × B ) ∪ ( C × D ) 6 = ( A ∪ C ) × ( B ∪ D ). You do not have to provide a proof that your example works, a picture or similar justiﬁcation will be suﬃcient. (Hint: Try intervals on the real line.)...
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This note was uploaded on 03/05/2011 for the course MATH 290 taught by Professor Alligood,k during the Fall '08 term at George Mason.
 Fall '08
 Alligood,K
 Math, Advanced Math

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