1. Construct a truth table for the expression p ® ~q Ú r.

p

q

r

            p

®

~q

Ú

r    

T

T

T

 

T

F

T

 

T

T

F

 

F

F

F

 

T

F

T

 

T

T

T

 

T

F

F

 

T

T

T

 

F

T

T

 

T

F

T

 

F

T

F

 

T

F

F

 

F

F

T

 

T

T

T

 

F

F

F

 

T

T

T

 

 

 

 

 

3

1

2

 

 

  1. Show whether p ® ~q Ú r º (p ® ~q) Ú r using truth tables. Justify your conclusion.
    The expressions are equivalent as they have the same truth tables.

p

q

r

p ® ~q Ú r

(p 

®

~q)

Úr

 

T

T

T

T

 

 

F

F

T

 

T

T

F

F

 

 

F

F

F

 

T

F

T

T

 

 

T

T

T

 

T

F

F

T

 

 

T

T

T

 

F

T

T

T

 

 

T

F

T

 

F

T

F

T

 

 

T

F

T

 

F

F

T

T

 

 

T

T

T

 

F

F

F

T

 

 

T

T

T

 

 

 

 

From #1

 

 

2

1

3

 

 

  1. Use Theorem 1.1.1 to show that ~(~p Ú q) Ú (p Ù q) º p. (Show your work, you do not have to provide the name for each law you utilize.)

~(~p Ú q) Ú (p Ù q)

º

(~~p Ù ~q) Ú (p Ù q)

 

º

(p Ù ~q) Ú (p Ù q)

 

º

p Ù (~q Ú q)

 

º

p Ù t

 

º

p