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Homework Assignment for CMSC 250 - Fall 2002 - Prof. Jandelyn Dawn Plane, Assignments of Discrete Structures and Graph Theory

University of MarylandDiscrete Structures and Graph Theory
Prof. Jandelyn Dawn Plane

A homework assignment for a university course named cmsc 250, which was offered in the fall semester of 2002. The assignment includes problems related to logical statements, demorgan's laws, truth tables, and logical rules. Students are required to write the solutions on paper and submit them in class.

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Pre 2010

Uploaded on 02/13/2009

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CMSC250-Homework2-Fall2002
DueWednesdaySept18thatthebeginningofyourdiscussionsection
Youmustwritethesolutionstotheproblemssingle-sidedonyourownlinedpaper,withallsheets
stapledtogether,andwithallanswerswritteninsequentialorderoryouwilllosepoints.
1. FindthenegationofthefollowingstatementsusingDeMorgan’slaws:
(a)FredandEthylarebothtelevisionstars
(b)PatisatelevisionstarbutSamisamoviestar
(c)AtelevisionshowcanstareitherRichardorKurtbuttheywillnotworktogether
2. ExpressandcompletelysimplifythenegationofthefollowingstatementsusingDeMorgan’slaws:
(a)x<y<z
(b)a>bandb<c
(c)x=3ory≥x
3. Foreachofthefollowingstatementsgive(i)theconverse,(ii)theinverse,and(iii)thecontrapositive:
(a)IfitisWednesdaythenitmustbeOctober
(b)Ifyouarenotcarefulwhenyoudriveyouwillgetintoanaccident
(c)IfItellbadjokesmystudentswilllaugh
4. Writethetruthtablefor~(p
~q)∧(q∨~r).Listalltriplesoftruth-valuesfor(p,q,r)thatmakethestatementfalse.
5. Writethisstatement’struthtable:(p∨q)↔(~p∧~(q∨p))
6. Foreachofthefollowing,statethenameoftherulefromTheorem1.1.1(Page14)orTable1.3.1(Page39)thatwould
beusedtogodirectlyfromthegivenstatement(s)tothegivenconclusionorwrite“invalid”ifthereisnosuchrule.
(a) statement: ~a∨(b∧(c∨d))
conclusion: (~a∨b)∧(~a∨(c∨d))
(b) statement: (a∧b)∧((a∧b)∨c)
conclusion: a∧b
(c) statements: a
b
~a
conclusion: ~b
(d) statements: (a∧b)
c
~c
conclusion: ~(a∧b)
(e) statements: a
b
a
c
conclusion: b
c

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Download Homework Assignment for CMSC 250 - Fall 2002 - Prof. Jandelyn Dawn Plane and more Assignments Discrete Structures and Graph Theory in PDF only on Docsity!

CMSC 250 - Homework 2 - Fall 2002

Due Wednesday Sept 18

th

at the beginning of your discussion section

You must write the solutions to the problems single-sided on your own lined paper, with all sheets

stapled together, and with all answers written in sequential order or you will lose points.

  1. Find the negation of the following statements using DeMorgan’s laws:

(a) Fred and Ethyl are both television stars (b) Pat is a television star but Sam is a movie star (c) A television show can star either Richard or Kurt but they will not work together

  1. Express and completely simplify the negation of the following statements using DeMorgan’s laws:

(a) x < y < z (b) a > b and b < c (c) x = 3 or y ≥ x

  1. For each of the following statements give (i) the converse, (ii) the inverse, and (iii) the contrapositive:

(a) If it is Wednesday then it must be October (b) If you are not careful when you drive you will get into an accident (c) If I tell bad jokes my students will laugh

  1. Write the truth table for ~(p

~q) ∧ (q ∨ ~r). List all triples of truth-values for (p, q, r) that make the statement false.

  1. Write this statement’s truth table: (p ∨ q) ↔ (~p ∧ ~(q ∨ p))
  2. For each of the following, state the name of the rule from Theorem 1.1.1 (Page 14) or Table 1.3.1 (Page 39) that would be used to go directly from the given statement(s) to the given conclusion or write “invalid” if there is no such rule.

(a) statement: ~a ∨ (b ∧ (c ∨ d)) conclusion: (~a ∨ b) ∧ (~a ∨ (c ∨ d)) (b) statement: (a ∧ b) ∧ ((a ∧ b) ∨ c) conclusion: a ∧ b (c) statements: a

b ~a conclusion: ~b (d) statements: (a ∧ b)

c ~c conclusion: ~(a ∧ b) (e) statements: a

b a

c conclusion: b

c