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Unformatted text preview: Math 1090 W08 Midterm Exam Solutions (1) Prove ` ( A β§ B β C ) β‘ ( A β ( B β C )). (You cannot use Postβs theorem, but you can use any of the proof methods covered so far.) Solution. A β ( B β C ) β (2.4.11) Β¬ A β¨ ( B β C ) β (2.4.11) Β¬ A β¨ Β¬ B β¨ C β (2.4.4) Β¬Β¬ ( Β¬ A β¨ Β¬ B ) β¨ C β (2.4.17) Β¬ ( A β§ B ) β¨ C β (2.4.11) A β§ B β C (2) Prove ` ( A β¨ B β¨ C ) β§ ( A β D ) β (( B β D ) β§ ( C β D ) β D ) (You cannot use Postβs theorem, but you can use any of the proof methods covered so far.) Solution. Assume A β¨ B β¨ C and A β D . By the Deduction Theorem, it suffices to prove ( B β D ) β§ ( C β D ) β D . Assume B β D and C β D . By the Deduction Theorem, it suffices to prove D . (1) A β D (assumption) (2) B β D (assumption) (3) C β D (assumption) (4) A β¨ B β¨ C (assumption) (5) A β¨ B β D β¨ D (1), (2), (2.5.10) (6) A β¨ B β D (5), axiom (7) (7) A β¨ B β¨ C β D β¨ D (3), (6), (2.5.10) (8)...
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This note was uploaded on 05/09/2010 for the course LAPS CSE 1090 taught by Professor Peter during the Winter '10 term at York University.
 Winter '10
 Peter

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