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