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CMSC 250

Quiz #3

Wednesday, Sept. 15, 2004

1. [12 pnts.] Prove that the following argument is valid by using the rules. Apply only the rules from Theorem 1.1.1 and Table 1.3.1 and the other things listed on the ``cheat sheet''. You must tell the name of the rule as you apply it and what line numbers contained the statements used to apply the rule.

   P1	$q \vee \sim p$
   P2	$r \rightarrow \sim q$
   P3	$p \rightarrow r$
   	therefore $\sim p$

   #	Statement	Rule	Lines Used
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   11
   12
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   14

   
   
   
   
   
   $\downarrow$ TURN OVER $\downarrow$
2. [12 pnts.] Prove that the following argument is valid by using the rules. Apply only the rules from Theorem 1.1.1 and Table 1.3.1 and the other things listed on the ``cheat sheet''. You must tell the name of the rule as you apply it and what line numbers contained the statements used to apply the rule.

   P1	$p \vee r$
   P2	$\sim (q \wedge \sim r)$
   	therefore $(p \rightarrow q) \rightarrow r$

   #	Statement	Rule	Lines Used
   1
   2
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   11

3. [6 pnts.] For each of the following identify the ONE SINGLE rule being applied or tell that it is not one of those listed on the ``cheat sheet''.

   1. If I stay up late at night, then I will be tired in the morning.
      I am not tired this morning.
      Therefore I did not stay up late last night.

      
      
      
      
      

   2. Either I study or I like football.
      If I like football, then I like mathematics.
      If I don't study, then I like mathematics.

      
      
      
      
      

   3. If I work hard, then I earn lots of money.
      If I earn lots of money, then I pay high taxes.
      If I pay high taxes, then I have worked hard.

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