HSS 2016 Solutions to Problem Set II-1

HSS 2016 Solutions to Problem Set II-1 - Deductive Logic Dr...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Deductive Logic Dr. James Pearson Solutions to Problem Set II 1. a) p q –p –q –p . –q p q –(p q) Since the last column is different to the fifth column on both the second and fourth rows, these schemata are not logically equivalent. [Note, you could have determined this after completing just two rows of the table.] b) p q –p –q p q – (p q) p . –q –p . q (p . –q) (–p . q) Since the fifth column and the last column are identical, these schemata are logically equivalent. c) p q r p . q q r (p . q) r p (q r) Since the final two columns are identical, these schemata are logically equivalent.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2. (a) p q r –r p . –r q . –r (p . –r) (q . –r) p q ß !!! ß !!! In the third and fifth rows, the first schema is true while the second schema is false, so the first schema does not imply the second. A truth-value assignment establishing the failure is where “p” and “r” are both true, and “q” is false. Another is where p” is false, and both “q” and “r” are true. [Note, you could have determined this after completing just three rows of the table.] (b) p q r –p q r q . r p (q r) –p (q . r) ß !!! Since in the last row, the first schema is true while the second schema is false, the first schema does not imply the second. A truth-value assignment exhibiting this failure is where “p”, “q”, and “r” are all false. (c) p q r p q –(p q) r . q – (p q) (r .q) q r ß !!! ß !!!
Image of page 2
In the second and sixth rows, the first schema is true while the second schema is false, so the first schema does not imply the second.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern