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

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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 different strings can be made from the word PEPPERER such that the strings begin and end with different letters? Zero or more of the following statements are may be correct. )( 6 3 )( 3 2 ) Problem 3. Zero or more of the following statements are true. Which ones are they? ( n k ) ( 3 2 ) k = ( 5 2 ) n ) = n ( n 1)2 n 2
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( m r k )( n k ) = ( m r + n ) ( n k ) 3 = ( 3 n n )
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