Documents

BIT11103+T2

Description
Subject Code Subject BIC 10103 / BIT 11003 Discrete Structure Item No. Tutorial 02 Date FSKTM Objective : 1) To introduce the concept Conjunctive Normal Form, CNF and Disjunctive Normal Form, DNF. 2) Understand the concept of predicate and quantifiers NAME : ……………………………………………………. MATRIC NO. : ……………………………………………………. A CNF (Conjunctive Normal Form) is a compound proposition in the form conjunctions of disjunctions of propositional variables or their negations, for example (pq) (p q)
Categories
Published
of 3
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
    FSKTM Subject Code BIC 10103 / BIT 11003 Item No. Tutorial 02 Subject Discrete Structure Date Objective : 1) To introduce the concept Conjunctive Normal Form, CNF and Disjunctive Normal Form, DNF. 2) Understand the concept of predicate and quantifiers NAME : …………………………………………………….  MATRIC NO. : …………………………………………………….    A CNF (Conjunctive Normal Form) is a compound proposition in the form conjunctions of disjunctions of propositional variables or their negations, for example (p  q)  (p   q)  (  p   q). Similarly a DNF (Disjunctive Normal Form) is disjunctions of conjunctions, such as  p   q   r)  (  p   q  r)  (  p  q   r). We say that the normal form is full when no variable is missing in each bracket. Theorem:  Every compound proposition is equivalent to a CNF and to a DNF. Example:  Convert [(p  q)   p]   q to a CNF and to a DNF. Solution:  First draw the truth table. The result is p q …  [(p  q)   p]   q T T …  F T F …  T F T …  F F F …  T  A full CNF can be obtained by selecting the variables with false values from each row of the table whose result is false: (  p   q)  (p   q) and similarly a full DNF from the true: (p   q)  (  p   q). Both forms are equivalent to the given proposition: [(p  q)   p]   q  (  p   q)  (p   q)  (p   q)  (  p   q). 1. Convert each proposition to a CNF and to a DNF. a)  (p  q)  p b) (p   q)  (  p  q) c) (p  q)  r d) [(p  q)  r]  [  p  (q  r)]  2. Convert each CNF to DNF and vice versa. a) (p  q)  (  p  q) b) (p  q)  (p   q)  (  p   q) c)  p   q   r)  (  p   q  r)  (  p  q   r)  (  p   q   r) d) (p   q  r)  (  p  q  r)   3.   Let L(x,y)  bethepredicate x  likesy, andlettheuniverseofdiscoursebethesetofallpeople.Usequantifierstoexpresseachofthefollowingstatements.a)Everyonelikeseveryone.b)Everyonelikessomeone.c)Someonedoesnotlikeanyone.d)EveryonelikesGeorge.e)Thereissomeonewhomeveryonelikes.f)Thereisnoonewhomeveryonelikes.g)Everyonedoesnotlikesomeone.4.   Let S(x)  bethepredicate x  isastudent,  B(y)  thepredicate  y isabook, and H(x,y)  thepredicate x  has  y  , wheretheuniverseofdiscourseistheuniverse,thatisthesetofallobjects.Usequantifierstoexpresseachofthefollowingstatements.a)Everystudenthasabook.b)Somestudentdoesnothaveanybook.c)Somestudenthasallthebooks.d)Noteverystudenthasabook.e)Thereisabookwhicheverystudenthas.f)Alihasamathbook.5.Let B(x)  , E(x)  and G(x)  bethestatements x  isabook,  x  isexpensive, and x  isgood, respectively.Expresseachofthefollowingstatementsusingquantifiers;logicalconnectives;and B(x)  , E(x)  and G(x)  ,wheretheuniverseofdiscourseisthesetofallobjects.a)   Nobooksareexpensive.b)    Allexpensivebooksaregood.c)   Nobooksaregood.d)   Does(c)followfrom(a)and(b)?  6.Let G(x)  , F(x)  , Z(x)  ,and M(x)  bethestatements x  isagiraffe,  x  is15feetorhigher, x  isinthiszoo, and x  belongstome, respectively.Supposethattheuniverseofdiscourseisthesetofanimals.Expresseachofthefollowingstatementsusingquantifiers;logicalconnectives;and G(x)  , F(x)  , Z(x)  ,and M(x)  .a)   Noanimals,exceptgiraffes,are15feetorhigher;b)   Therearenoanimalsinthiszoothatbelongtoanyonebutme;c)   Ihavenoanimalslessthan15feethigh.d)   Therefore,allanimalsinthiszooaregiraffes.e)   Does(d)followfrom(a),(b),and(c)?Ifnot,isthereacorrectconclusion?
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks