{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mt1-f03-sol

mt1-f03-sol - CS 70 Discrete Mathematics for CS Fall 2003...

This preview shows pages 1–4. Sign up to view the full content.

CS 70 Discrete Mathematics for CS Fall 2003 Wagner MT1 Solutions P RINT your name: , (last) (first) S IGN your name: P RINT your username on cory.eecs : W RITE your section number (101 or 102): This exam is open-book, open-notes. No calculators are permitted. Do all your work on the pages of this examination. If you need more space, you may use the reverse side of the page, but try to use the reverse of the same page where the problem is stated. You have 80 minutes. There are 4 questions, worth 25 points each (100 points total). The questions are of varying difficulty, so avoid spending too long on any one question. Do not turn this page until the instructor tells you to do so. Problem 1 Problem 2 Problem 3 Problem 4 Total CS 70, Fall 2003, MT1 Solutions 1

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

View Full Document
Problem 1. [True or false] (25 points) Circle T RUE or F ALSE . You do not need to justify your answers on this problem. N denotes the set of natural numbers, { 0 , 1 , 2 ,... } . Z denotes the integers, { ..., - 2 , - 1 , 0 , 1 , 2 ,... } . (a) T RUE or False : If the implication P = Q is true, then its converse is guaranteed to be true, too. (b) True or F ALSE : w Z . x Z . y Z . z Z . w + x = y + z . (c) True or F ALSE : x N . p Z . p > 5 = x 2 1 ( mod p ) . (d) True or F ALSE : p Z . p > 5 = ⇒ ∃ x N . x 2 1 ( mod p ) . (e) True or F ALSE : If m is any natural number satisfying m 1 ( mod 2 ) , then the equation 2048 x 1 ( mod m ) is guaranteed to have a solution for x . CS 70, Fall 2003, MT1 Solutions 2
Problem 2. [Proof by Induction] (25 points) Prove by induction that n i = 1 i ( i - 1 ) 2 = ( n + 1 ) n ( n - 1 ) 6 holds for all n N .

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

mt1-f03-sol - CS 70 Discrete Mathematics for CS Fall 2003...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online