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Test 1 Solutions - W07/CS 191 Suggested Solutions to TEST...

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W07/CS 191 : Suggested Solutions to TEST ONE Discrete Structures I 2/15/2007 OPEN BOOK Name_____________________ There are 5 problems with 20 points each. 1 . Use truth tables to determine whether (   q   r  and   (   r ) are logically  equivalent or not.  Answer :  p     q      r   q q     r (   q   r  (   r ) T     T      T T T T T T     T      F T F F F T     F      T F T T T T     F      F F T T T F     T      T T T T T F     T      F T F F T F     F      T T T T T F     F      F T T F T Because the column for  (   q )     r   and  the  column for   p     ( q     r )  are not  identical they are not logically equivalent.  1
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2 Use mathematical induction to show that 3 divides  n 3  + 2 n  for integer  n    0.  Proof Induction basis. When  n  = 0, the statement is obviously true, since 3 | 0.  Inductive step.
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