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MACM 101 (86)
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Department
Math & Comp Sci
Course
MACM 101
Professor
Bobby Chan
Semester
Fall

Description
Macm  101  Assignment  2       Due:  Week  5  –  AT  THE  BEGINNING  OF  YOUR  CLASS   PLEASE  READ  CAREFULLY:  do  not  copy  the  work  of  other  students.    You  may  discuss  the   questions  in  this  homework  with  other  students  in  this  class,  but  you  must  provide  your   own  solutions.    Failure  to  do  so  will  result  in  a  grade  of  0  on  your  assignment.    Only  a   selected  number  of  questions  in  this  homework  will  be  marked.   Student  Number:                   Family  Name:         Given  (Preferred)  Name:                                       Date:                   Lateness  Policy:   -­‐ One  day  late  (from  beginning  to  your  class  –  24  hours):  10%  off   -­‐ Two  days  late:  20%  off   -­‐ Three  days  late:  30%  off   -­‐ Not  accepted  after  this  :(   Plagiarism:   Knowingly  or  unknowingly  present  as  one’s  work  the  ideas  or  writings  of  another   without  appropriate  acknowledgement  or  referencing.    This  includes,  but  is  not  limited   to:   -­‐ Paraphrasing  text  without  acknowledgement  of  the  source   -­‐ Copying  the  text  of  another  student’s  assignment  or  other  students’  assignments   -­‐ Copying  of  visual  representations   All  forms  of  cheating  and  plagiarism  could  result  in  a  grade  of  0  for  the  whole   assignment,  a  grade  of  “F”  for  the  course,  or  cancellation  of  enrollment.   I  have  certified  that  the  attached  assignment  is  my  own  work  according  to  the   plagiarism  statement  above:     Signed:                             Please  show  your  work.    The  answers  by  themselves  are  worth  very  little.   1. Write  each  of  the  following  arguments  in  symbolic  form.  Then  establish  the  validity   (or  invalidity)  of  the  argument.    If  valid,  give  a  proof  using  the  laws  of   logic/inference  (state  the  laws  used).  If  invalid,  give  a  counterexample:     a. If  Rachel  gets  the  executive  chef  position  and  works  hard,  then  she’ll  get  a   raise.  If  she  gets  a  raise,  then  she’ll  buy  a  new  car.  She  has  not  purchased  a   new  car.    Therefore,  either  Rachel  did  not  get  the  supervisor’s  position  or  she   did  not  work  hard.                                   b. If  there  is  a  chance  of  rain  or  her  hat  is  missing,  then  Sally  will  not  mow  her   lawn.  Whenever  the  temperature  is  over  35˚C,  there  is  no  chance  of  rain.   Today  the  temperature  is  37˚C  and  Sally  is  wearing  her  hat.  Therefore  Sally   will  mow  her  lawn.                                   2. What  relevant  (primitive  statement)  conclusion  or  conclusions  can  be  drawn  from   the  following  set  of  premises?  Explain  the  rules  of  inference  (logic)  used  to  obtain   the  conclusion.   i) I’m  either  good  or  evil  (but  not  both)   ii) I’m  not  evil   iii) If  I’m  evil,  then  I  will  be  successful                                                   3. Prove  or  disprove  the  following  statement:   If  ac≡bc  (mod  m)  where  a,  b,  c  and  m  are  integers  with  m≥2,  then     a≡b  (mod  m).      
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