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...2-2 Other Set Operations and Their Properties 1. Set Intersection
2.
Set Union
3.
Disjoint Sets
4.
Complement of A relative to B (Set difference of B and A)
2
Examples: Shade the portion of the Venn diagram that represents the set. 1.
A B
2...
...Math 1350 2-3, 2-4 Addition, Subtraction, Multiplication, and Division of Whole Numbers Natural numbers: N = {1, 2,3, 4,} Whole numbers: W = {0,1, 2,3, 4,} Closure: A set is closed under addition if adding in 2 elements in the set results in an eleme...
...Math 1350
5-4 Proportional Reasoning
Definitions: 1. ratio a comparison of quantities notation: pronunciation:
1 2
one to two NOT one half
Ratios must involve two quantities. For example, However,
2 cannot be simplified to 2. 1
4 2 can be simp...
...4-4 Prime and Composite Numbers Definitions 1. prime any positive integer with exactly two distinct positive factors 2. composite any positive integer with more than two factors Note: 1 is neither prime nor composite Factor Trees Use a factor tree ...
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Set Problem 5 Due Monday, Nov. 29. Formal Logic Math 430, Fall 2004 1. Which of the following rules are sound (proof or counterexample): (a) 1 1 2 2 (1 2 ) (1 2 ) y x x (b) (c) (d) if y fr ( x) x x x 2. Let S = {f } where f is a 2-place function symbol. Compute (v2 f v2 v2 = v0 ) v2 v0 f v0 v1 . v2 3. Let S be a symbol set, let x be a variable, and let t be an S-term. Show that for every S-formula : x (a) x = ; t (b) if x fr (), then x = . / (Proceed by induction on the construction of .) 4. Using the rules of the sequent calculus, show that the following two rules are derivable. as Here usual " " is shorthand for "( )". (Please turn.) 5. Let S = {R} where R is a 2-place relation symbol. Proof or counterexample: (a) yxRxy (b) yxRxy xyRxy xyRxy. 6. (Extra credit.) The rules of the sequent calculus depend on the choice of a symbol set S. Suppose that R is a 1-place relation symbol not in S and let be a sequent over S (i.e., not involving the symbol R). Show: if is derivable in the sequent calculus for S {R}, then is also derivable in the sequent calculus for S. (Hint: replace every occurrence of R in a derivation of inductively by the equation x = x.)
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UCLA >> MATH >> 506 (Spring, 2009)
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UCLA >> MATH >> 506 (Spring, 2009)
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UCLA >> MATH >> 430 (Fall, 2009)
Problem Set 4 Due Monday, Nov. 1. Formal Logic Math 430, Fall 2004 1. Let S be a symbol set and let M be an S-structure, and suppose that D and E are subsets of M m which are definable without parameters in M. (a) Show that DE, DE, and M m \\D are def...
UCLA >> MATH >> 506 (Spring, 2009)
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UCLA >> MATH >> 430 (Fall, 2009)
Problem Set 1 Due Friday, Sept. 17. Formal Logic Math 430, Fall 2004 1. Specify a symbol set appropriate for vector spaces over the rational numbers Q. 2. Let S be a symbol set. Show that every S-term has length > 0. 3. Compute the complexity Cp(t) ...
UCLA >> EE >> 202 (Fall, 2009)
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UCLA >> EE >> 116 (Winter, 2009)
2/1/2001 CMOS Technology EE116B (Winter 2001): Lecture #3 Mani Srivastava UCLA - EE Department mbs@ee.ucla.edu 2 Copyright 2001 Mani Srivastava Reading for this Lecture n http:/vlsi.wpi.edu/webcourse/ch02/ch02.html 3 Copyright 2001 Mani Sri...
UCLA >> EE >> 116 (Winter, 2009)
EE116B : VLSI Systems Design (Mani Srivastava) Winter 2001 Home Work #3 (due by 10 AM on March 1, 2001) Solutions NAME:_ Total = 10 + 10 + 15 = 35 points Notes: 1. 50% penalty for up to 2 hour late submission. Zero credit after that. 2. Please ans...
UCLA >> EE >> 206 (Fall, 2009)
EE206A Lecture #7 Mobility in Non Ad Hoc Wireless Networks Mani Srivastava mbs@ee.ucla.edu University of California at Los Angeles Electrical Engineering Department R E SI T Y O F C A NIV A LIF ORN EU L IG H T LE T H H 1868 Copyright 2001 ...
UCLA >> EE >> 206 (Fall, 2009)
Copyright 2001 Mani Srivastava Ad Hoc Wireless Networks Part I (MANET) EE206A (Spring 2001): Lecture #8 Mani Srivastava UCLA - EE Department mbs@ee.ucla.edu Note: Many slides are based on Mobicom 2000 tutorial by Nitin Vaidya, Texas A&M Universit...
Cal Poly Pomona >> RT >> 004747 (Fall, 2009)
Neuroimaging Studies of Memory John Jonides Tor D. Wager David T. Badre University of Michigan Address correspondence to: Dr. John Jonides Department of Psychology University of Michigan 525 E. University Ave. Ann Arbor, MI 48109-1109 Telephone: 734-...
Cal Poly Pomona >> RT >> 11 (Fall, 2009)
Neuroimaging Studies of Memory John Jonides Tor D. Wager David T. Badre University of Michigan Address correspondence to: Dr. John Jonides Department of Psychology University of Michigan 525 E. University Ave. Ann Arbor, MI 48109-1109 Telephone: 734-...
Cal Poly Pomona >> RT >> 004747 (Fall, 2009)
Galley: Article - 00567 Level 2 Linguistic Relativity CONTENTS Does language shape thought? Space Time Shapes and substances Objects Summary Lera Boroditsky, Massachusetts Institute of Technology, Cambridge, Massachusett, USA Article descriptor: L...
Cal Poly Pomona >> RT >> 11 (Fall, 2009)
Galley: Article - 00567 Level 2 Linguistic Relativity CONTENTS Does language shape thought? Space Time Shapes and substances Objects Summary Lera Boroditsky, Massachusetts Institute of Technology, Cambridge, Massachusett, USA Article descriptor: L...
Cal Poly Pomona >> ASTRO >> 6 (Fall, 2009)
Archeoastronomy and World Cosmology Astronomy 6, Spring 2008 Pomona College Short Assignment #4: Egypt and Greeks (due March 13, 2008) \"Material objects are of two kinds, atoms and compounds of atoms. The atoms themselves cannot be swamped by any fo...
UCLA >> HOTNETS >> 5 (Fall, 2009)
Forward Welcome to the 5th Workshop on Hot Topics in Computer Networks! We received 114 submissions. The ten members of the program committee submitted 421 reviews, and external reviewers submitted an additional six reviews. HotNets papers are shor...
Cal Poly Pomona >> MATH >> 04747 (Fall, 2009)
Math 152 Fall 2008 Jo Hardin warm-up # 13 Name: Assume weights of cereal in 10oz boxes are normally distributed, N (, 2 ), both unknown. To test whether or not the box label is accurate, we set up our hypotheses: H0 : = 10oz H1 : = 10oz Find th...
Cal Poly Pomona >> MATH >> 152 (Fall, 2009)
Math 152 Fall 2008 Jo Hardin warm-up # 13 Name: Assume weights of cereal in 10oz boxes are normally distributed, N (, 2 ), both unknown. To test whether or not the box label is accurate, we set up our hypotheses: H0 : = 10oz H1 : = 10oz Find th...
Cal Poly Pomona >> MATH >> 04747 (Fall, 2009)
Math 152 Fall 2008 Jo Hardin warm-up # 2 Name: Suppose that we want to estimate the true proportion of free-throws Shaquille O\'Neal can make. Unlike in class, however, we think we know a lot about his ability. From watching him play, it seems as tho...
Cal Poly Pomona >> MATH >> 152 (Fall, 2009)
Math 152 Fall 2008 Jo Hardin warm-up # 2 Name: Suppose that we want to estimate the true proportion of free-throws Shaquille O\'Neal can make. Unlike in class, however, we think we know a lot about his ability. From watching him play, it seems as tho...
Cal Poly Pomona >> MATH >> 04747 (Fall, 2009)
Professor Hardin Math 152 Fall 2006 warm-up # 9 Name: Back to the cereal example in class. Assume the weight of a 10 oz box of cereal is Normally distributed with mean and variance 2. To test whether or not the box is accurate (i.e., whether it re...
Cal Poly Pomona >> MATH >> 152 (Fall, 2009)
Professor Hardin Math 152 Fall 2006 warm-up # 9 Name: Back to the cereal example in class. Assume the weight of a 10 oz box of cereal is Normally distributed with mean and variance 2. To test whether or not the box is accurate (i.e., whether it re...
Cal Poly Pomona >> MATH >> 04747 (Fall, 2009)
Math 152 Fall 2007 Professor Hardin warm-up # 13 Name: Assume weights of cereal in a 10oz box are normally distributed. Test whether or not the box is accurate (no preconceived notion of directionality) at a size of 0.05. Also, approximate the p-val...
Cal Poly Pomona >> MATH >> 152 (Fall, 2009)
Math 152 Fall 2007 Professor Hardin warm-up # 13 Name: Assume weights of cereal in a 10oz box are normally distributed. Test whether or not the box is accurate (no preconceived notion of directionality) at a size of 0.05. Also, approximate the p-val...
Cal Poly Pomona >> MATH >> 04747 (Fall, 2009)
Math 152 Fall 2008 Jo Hardin warm-up # 15 Name: Suppose X1 , X2 , . . . , Xn N (0, 2 ), and it is desired to test: H0 : 2 2 H1 : 2 > 2 1. Find the UMP test at level 0 . 2. Assume n = 20, 0 = 0.01, find the power function for the test in part 1....
Cal Poly Pomona >> MATH >> 152 (Fall, 2009)
Math 152 Fall 2008 Jo Hardin warm-up # 15 Name: Suppose X1 , X2 , . . . , Xn N (0, 2 ), and it is desired to test: H0 : 2 2 H1 : 2 > 2 1. Find the UMP test at level 0 . 2. Assume n = 20, 0 = 0.01, find the power function for the test in part 1....
UCLA >> PROJ >> 4 (Fall, 2009)
The proj4 Package March 24, 2009 Version 1.0-4 Title A simple interface to the PROJ.4 cartographic projections library Depends R (>= 2.0.0) Author Simon Urbanek <simon.urbanek@r-project.org> Maintainer Simon Urbanek <simon.urbanek@r-project.org> Desc...
UCLA >> SOFTWAREDE >> 24 (Fall, 2009)
David Geffen School of Medicine 710 Westwood Plaza, Reed 4238 Los Angeles, California 90095 Phone: 310.206.2101 Fax: URL: 310.206.5518 www.ccb.ucla.edu Principal Investigators: Arthur W. Toga, PhD Tony F. Chan, PhD AGENDA CCB Software Development...
UCLA >> WCCFL >> 27 (Fall, 2009)
Covert A-Movement: New evidence from the Caucasus keywords: raising, covert movement Introduction. This paper explores a case of covert A-movement in Adyghe (Circassian), a Northwest Caucasian language spoken in Russia. We show that in subject-to-sub...
UCLA >> TASK >> 1 (Fall, 2009)
APEX-Task I Conference Call Summary Dec. 4, 2001 Participants: P. Fogarty, B. Kaita, B. Nelson, H. Huang, A. Ying, M. Youssef, M. Sawan (Note: Several task participants were at the HHF meeting.) Key Points and Action Items 1. On the proposed CMOD di...
Cal Poly Pomona >> CS >> 121 (Fall, 2009)
System Testing & Performance System Testing system testing vs. unit testing planning for system testing Unit vs. System Testing Goals is this component ready to integrate? is this system ready to ship? A1 Bug Finding bug detection rates re...
Cal Poly Pomona >> CS >> 190 (Fall, 2008)
Pomona College Department of Computer Science A Study of Keystroke Dynamics as a Practical Form of Authentication Charles Zhou May 1, 2008 Submitted as part of the senior exercise for the degree of Bachelor of Arts in Computer Science Professor Eve...
Cal Poly Pomona >> MATH >> 04747 (Fall, 2009)
Math 158, Spring 2009 Jo Hardin semester project (part 1) Data Description & Descriptive Statistics Your task for this project is to describe a set of data of your choice and to perform some basic statistical analyses. The report should include: Th...
Cal Poly Pomona >> MATH >> 158 (Fall, 2009)
Math 158, Spring 2009 Jo Hardin semester project (part 1) Data Description & Descriptive Statistics Your task for this project is to describe a set of data of your choice and to perform some basic statistical analyses. The report should include: Th...
Cal Poly Pomona >> ID >> 04747 (Fall, 2009)
Critical Inquiry Seminar ManifestversusScientificImage Writing Assignment Due Tues, Sept. 21 In the chapter we read, Stroud offers a (lengthy) point-by-point refutation of Austin. On pages 5372, Stroud discusses (at length) one part of Austins posit...
Cal Poly Pomona >> ID >> 104 (Fall, 2009)
Critical Inquiry Seminar ManifestversusScientificImage Writing Assignment Due Tues, Sept. 21 In the chapter we read, Stroud offers a (lengthy) point-by-point refutation of Austin. On pages 5372, Stroud discusses (at length) one part of Austins posit...
UCLA >> MEETING >> 4 (Fall, 2009)
APEX Mechanical Design Considerations for Liquid Wall Concepts presented by B. Nelson APEX Meeting Sandia National Laboratory July 27, 1998 Presentation Outline _ Status of Activities for mechanical design and availability group General Design Re...
UCLA >> MEETING >> 4 (Fall, 2009)
APEX Mechanical Design Considerations for Liquid Wall Concepts presented by B. Nelson APEX Meeting Sandia National Laboratory July 27, 1998 Presentation Outline _ Status of Activities for mechanical design and availability group General Design Re...
UCLA >> MEETING >> 2 (Fall, 2009)
NEW CONCEPTS FOR HIGH-POWER-DENSITY ENERGY EXTRACTION SYSTEMS Nasr M. Ghoniem Mechanical and Aerospace Engineering Department University of California, Los Angeles (UCLA) Los Angeles, CA. 90095-1600 APEX Meeting UCLA January 12, 1998 High Power d...
UCLA >> MEETING >> 2 (Fall, 2009)
Design Issues for UCLA Liquid Surface FW and Blanket Concepts UCLA Fusion Science and Technology Group Mohamed Abdou Anter El-Azab Neil Morley Alice Ying Mahmoud Youssef Advanced Power Extraction (APEX) Group Meeting University of California, Los A...
UCLA >> MEETING >> 1 (Fall, 2009)
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UCLA >> MEETING >> 1 (Fall, 2009)
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UCLA >> MEETING >> 6 (Fall, 2009)
Concept: Replace first wall, and blanket with a thick flowing liquid Thick Liquid Walls for the Advanced Tokamak Confinement Scheme Presented by Alice Ying APEX VI UCLA Feb. 17, 1999 Presentation Outline 1. 2. 3. 4. 5. Possible Options of \"Thick Liq...
UCLA >> MEETING >> 5 (Fall, 2009)
Progress on Gravity & Momentum Driven Thick Liquid Wall Concepts for High Power Density MFE FW/Blanket Designs Presented by Alice Ying APEX V UCLA Nov. 2, 1998 Presentation Outline 1. 2. 3. Considerations for Idea Conceptualization Progress on GMD w...
UCLA >> MEETING >> 16 (Fall, 2009)
Range of Blanket Concepts for Power Plants EVOLVE ARIES-AT DREAM Hybrid-HCPB ARIES-RS CREST DC steel/sic steel sic A-HCPB TAURO } solid breeder HCPB WCLL steel steel, sic insert sic v w } liquid metal breeder Development Risk (Extrapolation ...
UCLA >> MEETING >> 4 (Fall, 2009)
Tritium Breeding and Power Multiplication Issues in Liquid Wall Concepts Mahmoud Youssef UCLA Presented at APEX Group Meeting, SNL, July 27-29, 1998 APEX Meeting, SNL, July 27-29,98 Tritium Breeding and Power Mult. M.Z. Youssef Objective Assess t...
UCLA >> FORTRAN >> 95 (Fall, 2009)
Introduction to Object-Oriented Concepts using Fortran90 Viktor K. Decyk Department of Physics and Astronomy University of California, Los Angeles Los Angeles, CA 90095-1547 & Jet Propulsion Laboratory California Institute of Technology Pasadena, Cal...
UCLA >> FORTRAN >> 95 (Fall, 2009)
How to Express C+ Concepts in Fortran90 Viktor K. Decyk Department of Physics and Astronomy University of California, Los Angeles Los Angeles, CA 90095-1547 & Jet Propulsion Laboratory California Institute of Technology Pasadena, California 91109-809...
UCLA >> FORTRAN >> 95 (Fall, 2009)
Introduction to Object-Oriented Concepts in Fortran95 Object-Oriented Programming (OOP) is a design philosophy for writing complex software. Its main tool is the abstract data type, which allows one to program in terms of higher level concepts than j...
UCLA >> MATH >> 32 (Fall, 2008)
MATH 32A: MIDTERM II SOLUTIONS 1. (15 points) Find the limit, if it exists, or show that the limit does not exist. (a) (5 pts) x3 y + x6 . (x,y)(0,0) x6 + y 2 lim Solution. The limit along the line x = 0 is 0 and the limit along y = 0 is 1, so th...
UCLA >> MATH >> 32 (Fall, 2008)
Jared Weinstein, Instructor MS 5230 www.math.ucla.edu/jared jared@math.ucla.edu Math 32A Calculus of Several Variables U.C.L.A. Dept. of Mathematics Fall 2007 Practice Midterm II Solutions 2 (1) Let z = y 2 ex . Find dz. Solution. dz = 2xy 2 ex ...
UCLA >> STATS >> 596 (Fall, 2009)
Appendix 1, Part 2. Subjective Probability. We have assumed that the \"rational decision maker\" knows the exact probabilities of any lottery, p P , that is offered to him, as he would for example if the lottery were conducted using a roulette wheel....
Cal Poly Pomona >> CS >> 190 (Fall, 2008)
Pomona College Department of Computer Science VIBES: Visualizing Changing Emotional States in Blogs April Wensel May 1, 2008 Submitted as part of the senior exercise for the degree of Bachelor of Arts in Computer Science Professor Sara Owsley Sood,...
UCLA >> COMPLING >> 2 (Fall, 2009)
Marcus Kracht CompLing II, Spring 2007 Exercise Sheet 1 To be handed in on Thursday, April 19 Linear Context Free Rewrite Systems Exercise 1. Suppose that L A is a LCFRL and that v : A B is a map that assigns a B-string to each letter of A. v i...
UCLA >> LING >> 20 (Fall, 2008)
PROF. MARCUS KRACHT: LING 20. WINTER 2007. Assignment B [Week 2] (5 Points per exercise, do 4 out of 5 exercises) Exercise B.1. In English, [k] and [k] (plain velar and fronted velar stops, respectively) are allophones of the same phoneme. Consider t...
UCLA >> LING >> 20 (Fall, 2008)
PROF. MARCUS KRACHT: LING 20. WINTER 2007. Assignment D [Week 2] (5 Points per exercise, do 4 out of 5 exercises) Exercise D.1. Draw the phrase structure tree of the sentence The mouse quickly ate the cheese. Exercise D.2. Draw the phrase structure t...
UCLA >> LING >> 20 (Fall, 2008)
PROF. MARCUS KRACHT: LING 20. WINTER 2007. Assignment E (5 Points per exercise, do 4 out of 5 exercises) Exercise E.1. Give at least 3 examples involving A coordination. Exercise E.2. Consider the Fijian pronouns: au iko koya kedaru keirau kemudran r...
Cal Poly Pomona >> CS >> 081 (Fall, 2009)
Computer Science 81 Recursive Functions Fall Semester, 2008 The computable functions on the natural numbers are those that can be computed on a Turing machine. There are several other, equivalent denitions of computable functions, including the rec...
Cal Poly Pomona >> CS >> 10 (Fall, 2009)
Example CFG CS 181: Natural Language Processing Lecture 10: Parsing K i m B r u c e P o m o n a C o l l e g e S p r i n g 2 0 0 8 Disclaimer: Slide contents borrowed from many sources on web! T = {this, that, a, the, man, book, ight, meal, include, r...
Cal Poly Pomona >> CS >> 181 (Fall, 2008)
Example CFG CS 181: Natural Language Processing Lecture 10: Parsing K i m B r u c e P o m o n a C o l l e g e S p r i n g 2 0 0 8 Disclaimer: Slide contents borrowed from many sources on web! T = {this, that, a, the, man, book, ight, meal, include, r...
Cal Poly Pomona >> CS >> 30 (Fall, 2009)
Computer Science 30 Assignment 6 due at noon on Friday, March 13, 2009 These exercises extend the exploration of neural networks that we began in lab on March 6th. Think of each part as an experiment. Compare the results of several trials as you va...
Cal Poly Pomona >> LGCS >> 105 (Fall, 2009)
LGCS 105 Spring 2005 S. Harves CONSTITUENCY AND q-ROLES Due 2/23/2005 I. AMBIGUITY AND CONSTITUENCY TESTS Similar to the twinkie-sentence discussed in class, the following sentence is multiply ambiguous. 1. Spike staked the vampire in his hand with...
Cal Poly Pomona >> JDA >> 14747 (Fall, 2009)
DRAFT VERSION 12, 19 June 2005/rev. 10 October 2005, rev. February 2006, March 2006 10,660 words Qualia, Consciousness, and Memory: Dennett (2005), Rosenthal (2002), LeDoux (2002), and Libet (2004) 1 Lecture to the School of Behavioral and Cognitive ...
UCLA >> AAS >> 119 (Winter, 2006)
Resources for Class Projects KIWA Restaurant Workers Campaign http:/www.kiwa.org/e/homefr.htm \"Grassroots Rising: Asian Immigrant Workers in Los Angeles\" http:/www.vconline.org/grassroots/ Asian Pacific American Labor Studies: \"Grassroots Rising\" Pro...
UCLA >> AAS >> 119 (Winter, 2006)
Work Shouldn\'t Hurt, You Come First! Created by: Grace Chang, Yvonne Chen, Daniel Conde, Kristine Gonzales, Maria Kim, Victoria Le, Christopher Lee, Steven Lee, Brian Lim, Ka Ki Hubert Ng, Lynne Nguyen, Mina Song, Helen Tang, Kristine Tapia, Lin Ann...
UCLA >> CS >> 194 (Fall, 2009)
CS Honors Undergraduate Research Program Faculty Coordinator: Prof. Amit Sahai Deborah Estrin Fall 2007 Spring 2008 Fall 2008 - Spring 2009 U.C.L.A. 1 Tuesday, October 7, 2008 1 What is the Honors Research Program? Your own creative research: Ind...
UCLA >> SENSYS >> 03 (Fall, 2009)
TOSSIM: Accurate and Scalable Simulation of Entire TinyOS Applications Philip Levis , Nelson Lee , Matt Welsh , and David Culler {pal,culler}@cs.berkeley.edu, mdw@eecs.harvard.edu Computer Science Division Intel Research: Berkeley Harvard Universit...
UCLA >> CS >> 118 (Fall, 2009)
Chapter 5 Link Layer and LANs These slides are based heavily on slides provided by the authors of the book and all material should be considered as belonging to their copyright. However, I have made changes, deletions, and additions to their slides; ...
UCLA >> MEETING >> 3 (Fall, 2009)
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UCLA >> MEETING >> 2 (Fall, 2009)
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