CIS 125

07 Conditional Propositions and Truth Tables

 

Note: The tilde (~) may be 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, evaluate each proposition for the truth values where p is false, q is true, and r is false.

 

1. p q

 

 

2. p q

 

 

3. (p q)

 

 

 

4. (p q) ^ (q r)

 

 

 

 

5. (p q) r

 

 

 

 

For problems 6-10 use truth tables to determine if each pair of propositions is equivalent. Identify whether they are, in fact, equivalent.

 

6. p

p ^ q

e.g. is p equivalent to p ^ q for every combination of truth values of p and q?

 

 

 

 

 

7. p ^ q

p v q

 

 

 

 

 

8. p q

p v q

 

 

 

 

 

9. p q

q p

 

 

 

 

 

10. (p q) ^ (q r)

p r

 

 

 

 

 

 

Formulate the symbolic expression in words using the following text:

p: Today is Tuesday

q: it is raining

r: it is cold

 

11. p q

 

 

 

 

 

12. q (r ^ p)