Test 1 Solutions

# Test 1 Solutions - F06/CS 191 Suggested Solutions to TEST...

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F06/CS 191 : Suggested Solutions to TEST ONE Discrete Structures I 9/28/2006 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   r (   q  (   r )   r  (   r ) T     T      T T T T T T T     T      F T F T T T T     F      T F T T T T T     F      F F F F F F F     T      T T T T T T F     T      F T T T T T F     F     T T T T T T F     F     F T T T F T Because the column for (   q  (   r ) and column for   (   r ) have identical  values, (   q  (   r ) and   (   r ) are logically equivalent.  1

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2 Prove that 7 n -1 – 1 is divisible by 3 for all n 1 by induction. Answer:
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Test 1 Solutions - F06/CS 191 Suggested Solutions to TEST...

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