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Unformatted text preview: Homework 1, (carries no grade - solutions will be posted in 1 week) 1. (i) Convert the following into logical notation using suggested vari- ables. Then provide a formal proof. If (l)I study law, then (m)I will make a lot of money. If (a)I study archaeology, then (t)I will travel a lot. If I make money or travel a lot, then I will not be disappointed. Therefore, If I am disappointed, then I did not study law and I did not study archaeology. Example: Either (p)Pat did it, or (q)Quincy did it. Quincy could not (r)have been reading and done it. Quincy was reading. Therefore Pat did it. Solution: axioms: p ∨ q, ¬ ( r ∧ q ) , r. need to prove: p proof: ¬ ( r ∧ q )(given) ⇒ ( ¬ r ∨ ¬ q )(1). ( ¬ r ∨¬ q )(1) ∧ r (given) ⇒ ( ¬ r ∧ r )( ↑ ) ∨ ( ¬ q ∧ r ) ⇒ ¬ q ∧ r ⇒ ¬ q (2). ( p ∨ q )(given) ∧¬ q (2) ⇒ ( p ∧¬ q ) ∨ ( q ∧¬ q )( ↑ ) ⇒ ( p ∧¬ q ) ⇒ p. ♣ (ii) Can you prove, using the above axioms, that “if I am disappointed, then I studied mathematics”? Answer yes or no, and explain why.then I studied mathematics”?...
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- Spring '08
- Logic, Formal language, Book Exercise, REF LECT