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    Mzumbe University Faculty of Science and Technology MSS 111:foundational Analysis Tutorial Sheet 3

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    CHRISTIAN GERALD
    This document contains 24 logic and reasoning problems involving determining the validity of arguments through symbolic logic, counterexamples, or other logical reasoning techniques. The problems cover a range of topics including conditional statements, biconditional statements, disjunction, conjunction, quantifiers, and more. Students are asked to use principles of logic to analyze the structure and meaning of arguments.

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    Mzumbe University Faculty of Science and Technology MSS 111:foundational Analysis Tutorial Sheet 3

    Uploaded by

    CHRISTIAN GERALD
    121 views2 pages
    This document contains 24 logic and reasoning problems involving determining the validity of arguments through symbolic logic, counterexamples, or other logical reasoning techniques. The problems cover a range of topics including conditional statements, biconditional statements, disjunction, conjunction, quantifiers, and more. Students are asked to use principles of logic to analyze the structure and meaning of arguments.

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    Tutorial 3

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    This document contains 24 logic and reasoning problems involving determining the validity of arguments through symbolic logic, counterexamples, or other logical reasoning techniques. The problems cover a range of topics including conditional statements, biconditional statements, disjunction, conjunction, quantifiers, and more. Students are asked to use principles of logic to analyze the structure and meaning of arguments.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    121 views2 pages

    Mzumbe University Faculty of Science and Technology MSS 111:foundational Analysis Tutorial Sheet 3

    Uploaded by

    CHRISTIAN GERALD
    This document contains 24 logic and reasoning problems involving determining the validity of arguments through symbolic logic, counterexamples, or other logical reasoning techniques. The problems cover a range of topics including conditional statements, biconditional statements, disjunction, conjunction, quantifiers, and more. Students are asked to use principles of logic to analyze the structure and meaning of arguments.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    MSS 111 SEM 1 2015/2016 1

    Mzumbe University
    Faculty of Science and Technology
    MSS 111:Foundational Analysis
    Tutorial sheet 3:

    Fallacies and Valid Arguments


    1. Prove the validity of the following argument. \If you send me an email message, then I will nish writing the
    program ". \If you do not send me an email, then I will go to sleep early ". \If I go to sleep early, then I will wake
    up feeling refreshed ". Therefore, \If I do not nish writing the program, then I will wake up feeling refreshed ".

    2. By the principle of demonstration show whether the following argument is valid or not: \If I eat pizza, then I
    will drink soda or beer. I will eat pizza. I will not drink beer. Therefore, I will drink soda."

    3. By counterexample show that this particular argument is valid or invalid. \If I shot you or stabbed you, then
    you died. I did not stab you. You died. Therefore, I shot you."

    4. By the rules of inference show that the following hypotheses \Jasmine is skiing or it is snowing"and \It is snowing
    or Bart is playing hockey"lead to the conclusion that \Jasmine is skiing or Bart is playing hockey".

    5. Are the following arguments valid?

    a) \If you do every problem in this book, then you will learn discrete mathematics. You learned discrete
    mathematics. Therefore, you did every problem in this book".
    b) \If you do every problem in this book, then you will learn discrete mathematics. You did not learn discrete
    mathematics. Therefore, you did not do every problem in this book".

    6. Show that \Everyone in this foundations analysis class has taken a course in computer science"and \Clara is a
    student in this class"lead to the conclusion that \Clara has taken a course in computer science".

    7. Show the validity of the following argument: A student in this class has not read the book. Everyone in this
    class passed the rst test. Therefore, someone who passed the rst test has not read the book.

    8. Use demonstration principle to prove the validity of the following argument: If I am paid, then I will buy you a
    present.If I will buy you a present, then you will be happy. Therefore, If I am paid, then you will be happy.

    9. Determine whether the following argument is valid: \The le is either a binary le or a text le. If it is a binary
    le then my program wont accept it. My program will accept the le. Therefore the le is a text le."

    10. Express the following argument in symbolic form and test its validity using the laws of logic: `If n > 10 when the
    subroutine call statement is reached, then the subroutine is called. The subroutine is called. Therefore n > 10
    when the subroutine call statement is reached.'

    11. Express the following argument in symbolic form and test its validity using the laws of logic: `Sandra is studying
    Computing or Sandra is not studying Accounting. If Sandra is studying Accounting then Sandra is not studying
    Computing. Therefore Sandra is studying Computing.'

    12. Show that p !( _p f )is a tautology.

    13. Use the principle of demonstration to prove the validity of the following arguments

    a) [(p ! )^( ! )^ ] !
    q q r p r

    b) [(p _ )^( !: )^( !


    q q p p q )] ! q
    MSS 111 SEM 1 2015/2016 2

    c) [(p ! ) ^ ( ! : )] ! ( ! :
    q r q p r )
    d) [(q _: )^: ] ! .
    p q p

    14. Which of the following are logically correct?

    a) [p ! ( _ )] ! ( ! ) ( ) [ _ ( ^ )] 
    q r p q c p p q p

    b) [p _ ( ^ )] ! ( ! ) ( ) [( ! ) ^ : ] ! :
    p q p r d p q p q

    15. Use laws of logic to simplify the expression p _ : (: ! p q ).

    16. Use laws of logic to show that [(p ! )^:


    q q ] !: p is a tautology.

    17. Is this argument valid? \If Connie is elected president of Phi Delta sorority, then Helen will pledge that sorority.
    Helen did not pledge Phi Delta sorority. Therefore, Connie was not elected president of Phi Delta sorority."

    18. Use the demonstration principle to prove the validity of the following argument.
    p ! r; r ! s; t _ :s; :t _ u; :u ` :p.
    19. Demonstrate the validity of the following argument: If the band could not play rock music or the refreshments
    were not delivered on time, then the New Year's party would have been canceled and Alicia would have been
    angry. If the party were canceled, then refunds would have had to be made. No refunds were made. Therefore
    the band could play rock music.

    20. Establish the validity of the following argument.


    p ! r; :p ! q; q ! s ` :r ! s.
    21. Use the demonstration principle to prove the validity of the following argument.
    p ! q; q ! (r ^ s); :r _ (:t _ u); p ^ t ` u.
    22. For the universe of all people, consider the open statements and prove its validity. All mathematics professors
    have studied calculus. Leona is a mathematics professor. Therefore Leona has studied calculus.

    23. Let us consider the universe of all triangles in the plane in conjunction with the open statements. In triangle
    XYZ there is no pair of angles of equal measure. If a triangle has two sides of equal length, then it is isosceles.
    If a triangle is isosceles, then it has two angles of equal measure. Therefore triangle XYZ has no two sides of
    equal length. Prove the validity of this argument.

    24. Here we consider the universe to be made up of the entire student body at a particular college. Prove the validity
    of this argument: No junior or senior is enrolled in a physical education class. Mary Gusberti is enrolled in a
    physical education class. Therefore Mary Gusberti is not a senior.

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