e3 - . .+2n=n(n+1) (a) What are i. (2 points) p(1): ii. (2...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CSE 260 Exam3, November 14, 2005 Name: This exam has 3 pages and 10 problems totaling 100 points. This is closed book and closed notes. A student can bring in a 8 1/2x11 sheet of notes. 1. (5 points) What is the nth terms of the following sequence. 5,10,20,40,80,160,320,. . . 2. (5 points) Find the value of Σ 100 k =10 k Given Σ n k =1 k = n ( n + 1) / 2 3. (2 points) Evaluate the following: -77 mod 6 4. Answer the following true/false (a) (2 points) 29 8(mod 7) (b) (2 points) 31 -14(mod 3) 5. (10 points) Which positive integers between 20 and 30 are relatively prime to 20? 6. Indicate if the following sets are countable. if the set is countable, give the one-to-one correspondence between Z + and the set. (a) (5 points) Set of all odd positive integers. 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
(b) (5 points) Set of all odd integers. (c) (5 points) Set of all reals between 0 and 1. 7. Let p(n) be the proposition p(n): 2+4+6+8+ .
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . .+2n=n(n+1) (a) What are i. (2 points) p(1): ii. (2 points) p(2): iii. (2 points) p(n+1): (b) (10 points) Prove p(n) n by mathematical induction. 8. (10 points) p ( n ) : n 2 + 5 n + 1 is odd Prove p(n) n 1 by mathematical induction. 2 9. Following relation R is represented by a directed graph (digraph). A B C D (a) (5 points) Write the relation R as a set of elements of R R . (b) (12 points) Circle the appropriate properties below for the relation. refexive irrefexive symmetric antisymmetric asymmetric transi-tive (c) Find the powers R 2 , R 3 (5 points) R 2 = (5 points) R 3 = 10. Following relation is dened on the set A = { 1 , 2 , 3 , 4 } R = { ( a, b ) A A | a b (mod 2) } (a) (5 points) Give the relation R as a set. (b) (1 points) Is it an equivalence relation? 3...
View Full Document

This note was uploaded on 06/08/2009 for the course CSE 260 taught by Professor Saktipramanik during the Spring '08 term at Michigan State University.

Page1 / 3

e3 - . .+2n=n(n+1) (a) What are i. (2 points) p(1): ii. (2...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online