MAS111_09_assignment_06 - B )-( A ∩ C ). (d) ( A ∩ B )...

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NANYANG TECHNOLOGICAL UNIVERSITY MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 6 TUTORIAL DATES: 05, 06, 07/09/09 1. Let A = { 1 , 2 } , B = { 2 , 3 , 4 , 5 } , C = { 1 , 2 , 4 , 5 , 6 , 7 } , D = { 3 , 5 , 7 , 9 } , E = { 4 , 6 , 8 } , F = { 2 , 6 } . List the elements of the following sets: B C , B C , C - E , B 4 E , A B , A C , A ( B C ), ( C - B ) - A , ( C - A ) - B , P ( F ), ( A E ) - ( C E ), P ( E ) - P ( C ), ( B - A ) F . 2. Let A,B,C be any sets. Prove that ( A B ) C = ( A C ) ( B C ). 3. Let A,B,C be any sets. Prove that (a) ( A - B ) - C = ( A - C ) - B . (b) (( A c B c ) - A ) c = A . (c) A ( B - C ) = ( A
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Unformatted text preview: B )-( A ∩ C ). (d) ( A ∩ B ) ∪ C = ( A ∪ C ) ∩ ( B ∪ C ). 4. Prove that for any sets A,B and C , A 4 ( B ∪ C ) ⊆ ( A 4 B ) ∪ ( A 4 C ). 5. For all sets A,B,C , prove that if A 4 C = B 4 C , then A = B . 6. Prove that for all sets A,B,C , A 4 ( B 4 C ) = ( A 4 B ) 4 C ....
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This note was uploaded on 01/23/2011 for the course MAS 111 taught by Professor Drchansongheng during the Spring '10 term at Nanyang Technological University.

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