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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.
asked in Mathematical Logic by Boss (11.7k points) | 22 views

1 Answer

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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 (^)

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

answered by Junior (635 points)

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