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In this exercise we will show that the Boolean product of

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 35E Chapter 2.6

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 35E

Problem 35E

In this exercise we will show that the Boolean product of zero–one matrices is associative. Assume that A is an m × p zero–one matrix,B is a p × k zero–one matrix, and C is a k × n zero–one matrix. Show that A⊙ (B⊙C) = (A⊙B) ⊙C.

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EVALUATION FOR EXTRA CREDIT *** VAUGE review from prof HISTORY - Know timeline dates - Three M’s in definition of packaging (materials, methods, machinery) - Ancient and man-made packages - Industrial revolution o Can, celluloid, paperboard cartons - Late 20 century o 50’s 60’s, 70s, 80s, 90s - Trends - users and suppliers o users: consumer, industrial, institutional o suppliers: converters, machinery and services FUNCTIONS - contain - protect - inform/sell - utility of use* NOT IN TEXTBOOK - four levels o primary, secondary, tertiary, and quaternary - product o contents, environment, damage - inform/sell: o required, motivational, trade dress - utility of use: o consumer, retailer, shipper/distributer MATERIALS - paper and paper board – wood pulp, cellulose - metals o steel o aluminum - glass - plastic - paper o cellulose and lignin o thickness: paper vs paperboard 0.12”  point .014” = 14 point o what “plastic” comes from wood Cellophane o three ways to make pulp Mechanical, chemical, and semi-chemical o general procedure for paper/paperboard  Screen, squeeze and dry o Callenderig o Basis weight of paper o Etc. o Use for bending grade board o Three basic design styles for folding cartons o Tube, tray and hybrid - Testing Mulllen bursts and edge crush test - RSC Regular slotted container - Two basic styles of composite cans o Convolute and - METALS o Cans- steel and aluminum o Two basics kind of can: three and two pieces o Etc. o Plating weights measured in lbs/basebox o Three ways to seal the side seam of a three piece can  Weld, solder or adhesive o Bayer process – bauxite ot aluminum o Hall herlout process o Now thin is aluminum foil 6 mil o Is aluminum used for packaging as a pure metal NO o What happens to WVTR as thickness of foil decreases Why  Increases bc pinholes - GLASS o How to make glass bottles  Blow and blow, press and blow o Major ingredients o What is cullet o Two methods for making glass bottles o What is gob o What is annealing Why important o Parts of a bottle o Advantages/disadvantage - POLYMERS o What is gutta percha o What is the first synthetic plastic  Bakelite o Etc. o Name of chem reaction used to link monomers Polymerization o If you link different monomers o Know abbrev : HDPE, LDPE, PP, PET, PVC, PVDC(saran) o What is density Yield How related o Thermoset/thermoplastic o Cost- more specialized plastics are more costly  Since the basic structure of most common polymers are similar, what mades each one different  Side chains o What basic process is used for all types of forming methods  Extrusion – melting plastic o What are 2 ways to make film  Cast and ring die o What does orientation meant as it relates to film  Stretched to align molecules for strength o What is coextrusion and what is it used for  Blends different polymers, film, sheet and bottles o What is injection molding used for o What type of package does extrusion blow molding produce  Bottle o What is a parison  Hollow tube inflatd into bottle o How is wall thickness controlled during extrusion blow molding  Programmed parison o What types of package are made by injection bow molding  Bottles o Stretch blow molding  Bottles o What are two advantages of extrusion bow ad molding compare to IBM and ISBM  One mold and handles o Adv. 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Chapter 2.6, Problem 35E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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In this exercise we will show that the Boolean product of