Use De Morgan's laws to find the negation of the following statement.

 

Kwame will take a job in industry or go to graduate school.

 

   

Kwame will not take a job in industry and will not go to graduate school.

   

Kwame will take a job in industry and will not go to graduate school.

   

Kwame will not take a job in industry and will go to graduate school.

   

Kwame will take a job in industry and will go to graduate school.

   

Kwame will not take a job in industry or will not go to graduate school.

 

 

 

 

 

 

 

 

 

Complete the truth table for each of these compound propositions.


a) p→(¬qr)

p

q

r

¬q

¬qr

p→(¬qr)

T

T

T

   

T

T

F

   

T

F

T

 

  

T

F

F

   

F

T

T

   

F

T

F

   

F

F

T

   

F

F

F

   



b) ¬p→(qr)

p

q

r

¬p

qr

¬p→(qr)

T

T

T

   

T

T

F

   

T

F

T

   

T

F

F

   

F

T

T

   

F

T

F

   

F

F

T

   

F

F

F

   



c) (pq)pr)

p

q

r

¬p

pq

¬pr

(pq)pr)

T

T

T

    

T

T

F

    

T

F

T

    

T

F

F

    

F

T

T

 

   

F

T

F

    

F

F

T

    

F

F

F

    


d) (pq)qr)

 

p

q

r

¬q

pq

¬qr

(pq)qr)

T

T

T

    

T

T

F

    

T

F

T

    

T

F

F

    

F

T

T

    

F

T

F

    

F

F

T

    

F

F

F

    



e) p↔¬q)↔(qr)

p

q

r

¬p

¬q

¬p↔¬q

qr

p↔¬q)↔(qr)

T

T

T

     

T

T

F

     

T

F

T

     

T

F

F

     

F

T

T

     

F

T

F

     

F

F

T

     

F

F

F

     

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Show that each of these conditional statements is a tautology by completing the truth tables.


a) (pq)→p

p

q

pq

(pq)→p

T

T

  

T

F

  

F

T

  

F

F

  

 



b) q→(pq)

p

q

pq

q→(pq)

T

T

  

T

F

  

F

T

  

F

F

  

 



c) ¬p→(pq)

p

q

¬p

pq

¬p→(pq)

T

T

   

T

F

   

F

T

   

F

F

   

 



d) (pq)→(pq)

p

q

pq

pq

(pq)→(pq)

T

T

   

T

F

   

F

T

   

F

F

   

 



e) ¬(pq)→p

p

q

pq

¬(pq)

¬(pq)→p

T

T

   

T

F

   

F

T

   

F

F

   

 



f) ¬(pq)→¬q

p

q

pq

¬(pq)

¬q

¬(pq)→¬q

T

T

    

T

F

    

F

T

    

F

F

    

 

 

 

 

 

 

 

    • Posted: 5 years ago
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