B either randy or paul but not both are chatting c if

Info icon This preview shows pages 2–4. Sign up to view the full content.

View Full Document Right Arrow Icon
b. Either Randy or Paul but not both are chatting. c. If Abby is chatting, so is Randy d. Paul and Kevin are either both chatting, or neither is. e. If Heather is chatting than so are Abby and Kevin. Let A = Abby is chatting, H = heather is chatting, K = Kevin is chatting, P = Paul is chatting, R = Randy is chatting The premises are: (1) K V H (2) R P 2
Image of page 2

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

View Full Document Right Arrow Icon
(3) A R (4) P K (5) H (A Λ K) We start with making an assumption. If the assumption leads to a contradiction, than the negation of the assumption is true. However if the assumption does not lead to a contradiction, we cannot conclude anything. Assume H is true (6) H From (6) and (5) by MP we conclude (7) A (8) K From (8) and (4) we conclude (9) P From (7) and (3) we conclude (10) R From (10) and (2) we conclude (11) ~P This contradicts (9), therefore our assumption is false. Therefore we can conclude ~H: Heather is not chatting (12) ~H From (12) and (1) by DS we conclude (13) K From (13) and (4) we conclude (14) P From (14) and (2) we conclude (15) ~R From (15) and (3) we conclude (16) ~A Thus we have determined that Kevin and Paul are chatting, and the other three individuals are not chatting.
Image of page 3
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