CIS 125

13– Direct Proof

 

Note: The tilde (~) is used to denote a logical inversion, or NOT, operation.

The symbol v is used to represent the OR operator, while the ^ symbol represents the AND operator.

 

For problems 1-5, use truth tables to determine whether each argument is valid.

 

1.         p  r

            p  q

            ------------

                 p  (r ^ q)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.         p  (r v q)

            r  ~q

            ------------

             p  r

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.         p  r

            r  q

            ------------

             q

 

 

 

 

 

 

 

 

 

 

 

 

 

4.         ~r  ~p

            r

            ------------

             p

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.         p  r

            r  q

            p

            ------------

             q