midterm-solW08 - Math 1090 W08 Midterm Exam Solutions (1)...

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Unformatted text preview: Math 1090 W08 Midterm Exam Solutions (1) Prove ` ( A B C ) ( A ( B C )). (You cannot use Posts theorem, but you can use any of the proof methods covered so far.) Solution. A ( B C ) (2.4.11) A ( B C ) (2.4.11) A B C (2.4.4) ( A B ) C (2.4.17) ( A B ) C (2.4.11) A B C (2) Prove ` ( A B C ) ( A D ) (( B D ) ( C D ) D ) (You cannot use Posts theorem, but you can use any of the proof methods covered so far.) Solution. Assume A B C and A D . By the Deduction Theorem, it suffices to prove ( B D ) ( C D ) D . Assume B D and C D . By the Deduction Theorem, it suffices to prove D . (1) A D (assumption) (2) B D (assumption) (3) C D (assumption) (4) A B C (assumption) (5) A B D D (1), (2), (2.5.10) (6) A B D (5), axiom (7) (7) A B C D D (3), (6), (2.5.10) (8)...
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midterm-solW08 - Math 1090 W08 Midterm Exam Solutions (1)...

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