samex3d - Sample Exam 3 EECS 203 Winter 2007 You have two...

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

View Full Document Right Arrow Icon
Sample Exam 3 EECS 203 Winter 2007 You have two hours to complete this exam. You may use any information you have written on three 8 . 5” × 11” sheets of paper, but no other information. Leave at least one seat between yourself and other students. Problem 1. Zero or more of the following relations on the set of all UM undergraduates are reflexive, symmetric, and transitive. Which ones are they? (a) R = { ( x, y ) | x and y have taken, or are taking, EECS 203 } . (b) R = { ( x, y ) | x and y have the same last digit of their student ID number } . (c) R = { ( x, y ) | x ’s GPA is greater than y ’s GPA } . (d) R = { ( x, y ) | x and y are enrolled in the same college or live in the same dorm } . Problem 2. How many diFerent strings can be made from the word PEPPERER such that the strings begin and end with diFerent letters? Zero or more of the following statements are may be correct. (a) 6! / (2! · 2! · 2!) + 2 · 6! / (2! · 3!) (b) 8! / (3! · 3! · 2!) (c) 2(6! / (2! · 2! · 2!) + 6! / (2! · 3!) + 6! / (3! · 2!)) (d) ( 8 2 )( 6 3 )( 3 2 ) Problem 3. Zero or more of the following statements are true. Which ones are they? (a) n k =0 ( n k )( 3 2 ) k = ( 5 2 ) n (b) n k =0 k ( k 1) ( n k ) = n ( n 1)2 n 2
Background image of page 1

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

View Full DocumentRight Arrow Icon
(c) r k =0 ( m r k )( n k ) = ( m r + n ) (d) n k =0 ( n k ) 3 = ( 3 n n ) Problem 4. Consider the directed graph below, where L indicates the level of the graph and n indexes the vertices at a given level. DeFne an interior vertex at a given level to be any vertex with three inbound edges. ±inally, let
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/01/2008 for the course EECS 203 taught by Professor Yaoyunshi during the Winter '07 term at University of Michigan.

Page1 / 4

samex3d - Sample Exam 3 EECS 203 Winter 2007 You have two...

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