final - Discrete Structures CSCI-150 Spring 2015 Final Exam...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Discrete Structures. CSCI-150. Spring 2015. Final Exam. You are allowed to use a formula sheet: It should be a single standard sheet of paper (of Letter/A4 size). The formula sheet has to be handed in after the exam. For every problem, provide a reasonably complete argument supporting your answer. Answers with no explanation may be insufficient to get full credit. Problem 1 (3 pts) Prove the equivalence: ( a b ) ( b c ) ≡ ¬ b c Hint: you may need to use the identity law: ( ¬ x ) ( ¬ x ) T . Problem 2 (3 pts) Given the following recurrently defined sequence of integers: a 0 = 3 , a n = 5 a n - 1 + 8 Prove by induction that all elements in this sequence are congruent to 3 modulo 4, or in other words: n 0 : a n 3 ( mod 4) Problem 3 (3 pts) Show that if n is an integer than the remainder ( n 2 rem 4) = 1 or 0 . Hint: every integer is either even or odd. Problem 4 (3 pts) (a) Draw the Hasse diagram for the following partially ordered set: ( 10 , 14 , 15 , 21 , 30 , 42 , 70 , 105 , 210 , ) , where the partial order relation is the divisibility relation: x y
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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