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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
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