tut5 - of the right one and vice versa. A-( B ∪ C ) = (...

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Problems to Week 6 Tutorial — MACM 101 (Fall 2011) 1. For U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } let A = { 1 , 2 , 3 , 4 , 5 } , B = { 1 , 2 , 4 , 8 } , C = { 1 , 2 , 3 , 5 , 7 } , and D = { 2 , 4 , 6 , 8 } . Determine each of the follow- ing: a ) ( A B ) C b ) A ( B C ) c ) C D d ) C D e ) ( A B ) - C f ) A ( B - C ) g ) ( B - C ) - D h ) B - ( C - D ) i ) ( A B ) - ( C D ) Draw Venn diagrams for each of the expressions. 2. Prove each of the following using Venn diagrams. (Assume a universe U .) (a) If A B and C D , then A C B D and A C B D . (b) A B if and only if A B = . (c) A B if and only if A B = U . 3. Prove or disprove each of the following: (a) For sets A,B,C U , if A C = B C , then A = B . (b) For sets A,B,C U , if A C = B C and A C = B C , then A = B . 4. Prove that A - B = A B . 5. Prove that A Δ B = ( A B ) ( A B ). 6. Investigate the truth or falsity of the following using 3 methods: Venn diagrams, laws of set theory, and proving that the left side is a subset
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Unformatted text preview: of the right one and vice versa. A-( B ∪ C ) = ( A-B ) ∩ ( A-C ) . 7. Use the laws of set theory to establish that ( A ∩ B ) ∪ ( A ∩ C ) = ( A ∩ B ) ∪ ( A ∩ C ) . 8. Using the laws of set theory, simplify each of the following 1 (a) ( A ∩ B ) ∪ ( A ∩ B ∩ C ∩ D ) ∪ ( A ∩ B ), (b) ( A-B ) ∪ ( A ∩ B ). 9. Construct the power set of the set {∅ , { 1 } , {{ a }}} . 10. Let A,B,C,D be nonempty sets. Prove that A × B ⊆ C × D if and only if A ⊆ C and B ⊆ D . 11. Prove that A × ( B-C ) ⊆ ( A × B )-( A × C ). Does the equality holds? 2...
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This note was uploaded on 10/14/2011 for the course MACM 101 taught by Professor Pearce during the Spring '08 term at Simon Fraser.

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tut5 - of the right one and vice versa. A-( B ∪ C ) = (...

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