Kenneth Rosen Edition 7 Exercise 1.3 Question 8 (Page No. 35)

Question

Use De Morgan’s laws to find the negation of each of the following statements.

1. Kwame will take a job in industry or go to graduate school.
2. Yoshiko knows Java and calculus.
3. James is young and strong.
4. Rita will move to Oregon or Washington.

Answer 1

Let's break the sentences if we encounter conjunctions(and) or disjunctions(or) into 2 propositional statements namely (p & q) as follows:-

(a) p=Kwame will take a job in industry; q= Kwame will go to graduate school

(b)p=Yoshiko knows Java; q = Yoshiko knows Calculus

(c)p=James is young; q=James is strong.

(d)p=Rita will move to Oregon; q=Rita will move to Washington

Now, to find the negation of the sentences,we first combine p & q using connectives(conjunctions or disjunctions) and then apply DeMorgan's law:-

Note:- We denote or by (v) & and by (^)

 $a) \sim (p \vee q)=\sim p \wedge \sim q =Neither\ Kwame\ will\ take\ a\ job\ in\ industry\ nor\ will\ she\ go\ to\ graduate\ school \\ b)\sim(p \wedge q)=\sim p \vee \sim q = Either\ Yoshiko\ don't\ know\ Java\ or\ he\ don't\ know\ Calculus\\ c)\sim(p \wedge q)=\sim p \vee \sim q=Either\ James\ is\ not\ young\ or\ he\ isn't\ strong \\ d)\sim (p \vee q)=\sim p \wedge \sim q =Neither\ Rita\ will\ move\ to\ Oregon\ nor\ will\ she\ move\ to\ Washington$