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)