1. Let p, q, and r be the following statements:
p: Roses are red
q: The sky is blue
r: The grass is green
Translate the following statements into English
(a) p ^ q (b) p ^ (q v r) (c) q -> (p ^ r) (d) ( ~ r ^ ~ q) -> ~ p

2. Write in symbolic form using p, q, r, ~, ->, v, ^, where p, q, r represent the following statements:
p: A puppy is green-eyed
q: A puppy can be taught
r: A puppy loves toys

(a)If a puppy is green-eyed, then it cannot be taught
(b)If a puppy cannot be taught, then it does not love toys
(c)If a puppy loves toys, then either the puppy can be taught or the puppy is green-eyed.
(d)If the puppy is not green-eyed, then the puppy loves toys and the puppy can be taught.

3. Fill the headings of the following truth table using p, q, ~, ->, V, and ^.

pq(a)(b)
TTTF
TFTF
FTTF
FFFT

4. For each of the following conditionals, identify the antecedent and the consequent. Form the converse, inverse, and contrapositive.

(a)If I donÂ’t go to the movie, IÂ’ll study my math.
(b)Your car wonÂ’t start if you donÂ’t have gasoline in the tank.

5. Rewrite ~(p V q) using DeMorgan’s laws.

6. (a) Translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.

If Lillian passes the bar exam, then she will practice law.
Lillian will not practice law
———————————————————————-
.. Lillian did not pass the bar exam

7. Use an Euler diagram to determine whether the syllogism is valid or invalid
All actresses are beautiful
Some actresses are tall
——————————–
.. Some beautiful people are tall.

8. Construct a truth table for (~q^p)->~q