Fall 2005 - Popescu's Class - Exam 1

Fall 2005 - Popescu's Class - Exam 1 - Exam 1, Mathematics...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Exam 1, Mathematics 109 Dr. Cristian D. Popescu October t7, 2005 Name: Student ID: Section Number: Note: There are 3 problems on this exam. You wili not receive credit unless you show all your work. No books, calculators, notes or tables are permitted. I. (30 points) (1) Write formally the following statement: " For all strictly positive real num- bersr andy, thesum rlA+ylris atleast2". (2) Write the formal negation of the statement in (1) above. (3) Prove or disprove the statement x'l€ {R' t,) [v -) ("r) (e it 7),r tXt R.r.) > frt GI Q-)trr) (" ^ (b*|* 42) y rovt il* Sf^+c *a^+ l'n ( ^ ) ,l e R>o L +)- -z = TX %'^tt x ,le Q>o ) A \&^V q-:j' >o -tr^F S/t wi\\ Ulx Tti^ erRro)^.hQIRrJ XJ -f >" L+I \x Y +I T1 x'* f- zx Tt-*t- D
Background image of page 1

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

View Full DocumentRight Arrow Icon
II. (30 points) (1) Write formally the foilowing statement: "If r is an irrational real number, then z2 * r is an irrational real number." (2) Prove or disprove the statement in (1) above. c) t (\ \-- I 1(-Q R T* qf^k"^l-A \n tn) )\ tJ-* ' l'Je *;l\ q(^^ ^ {u^', \a T"-'.,\ lt'^* if s tr'-t3<'f'nt \ q \-" \^ '^"'lt;* + S"{ s+^J<'^ r'+ a'L'"-'re is Q,.)G4q)^3'+x€G) \2- 5n-= w\ "-\ q\ *- --) \* -\ --) ] \-eZ ) an = bqA . }"^"F^
Background image of page 2
T--"tr 5 n..- ?'R' ( \ a \o ^^)- f*,, - \.-j,^^*\*\ \-= [4'J -\)**ts '"'r* c) 1 -:=) s\ n- ;> 1'dL*',
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

Fall 2005 - Popescu's Class - Exam 1 - Exam 1, Mathematics...

This preview shows document pages 1 - 5. Sign up to view the full document.

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