1. Write out a truth table for three variables, p, q, and r. Include
columns for all of the following:
p
q
r
q Ú
r
q Å r
(q Ú r) Ù
p
¬((q Ù r) Ú
p)
(p Ú r) Ù
q
(q Ù r) Ú
(q
Å
p)
2. Write out a truth table for two variables, p and q. Include columns
for all of the following:
p
q
p Ú q
p Ù q
p ® q
q ® p
p « q
¬ q ® ¬ p
3. Using the propositions
P: The United States has a king.
Q: Oranges grow on trees.
Write each of the following in symbolic language and determine its
truth value.
a. Either oranges grow on trees, or the United States has a king, but not both.
b. If oranges grow on trees, then the United States has a king.
c. If the United States has a king, then oranges grow on trees.
d. The United States has a king iff oranges grow on trees.
e. If oranges do not grow on trees, then the United States does not have a king.
f. It is true that oranges grow on trees. It is also true that the United States has a king.
g. If it is not the case that oranges grow on trees, then the assertion
that the United States has a king cannot be true.
4. Using a truth table, show whether the statement
(p Ú
r)
Ù
q
º
p
Ú
(r
Ù ¬q)
is valid.
5. Using the laws of logic (i.e. DO NOT USE A TRUTH TABLE), show whether
the statement
A: (¬ ( P Ú
Q) Ù P) Ù
( ¬ ( P Ú ¬ Q) Ù
P ) = FALSE
is a tautology. If it is a tautology, give a proof.
If it is not a tautology, give a proof of that, and a counterexample.
This page copyleft 1999 Brian K. Hare.