MAT 300 Spring 2006
Dr. Zandieh
Homework #3 Solutions
Recall that the entire universe of dragons in Lidd consists only of Red Rationals, Grey Rationals,
Red Predators, and Grey Predators. However, some regions of Lidd may not contain all four
types.
For each of the following quartets of statements in 1-3, compare statements a, b and c to the
original bolded statement. Tell whether the statement is equivalent to the original statement (i.e.
they have the same truth table values), is a negation of the original statement (i.e. their truth
tables have opposite values) or neither.
Write appropriate truth tables columns to illustrate your solutions. Use statements labeled p, q
and combinations or negations of these. Please state what p and q represent in words for each
pair of statements. (Make sure that p and q represent sentences with a verb, not just sets or a
noun.)
1. There is a dragon in the coastal region who is a grey predator.
a. There is a dragon in the coastal region who is not red and not a rational. (equivalent)
b. All dragons in the coastal region are red and rational. (neither)
c. All dragons in the coastal region are red or rational. (negation)
Example of a truth table
Let p = There is a Dragon who is a predator
Let q = There is a Dragon who is grey
Then the bolded phrase is p
∧
q
a. is ~(~q) ~(~p) which is the same as q ∧
∧
p or p
∧
q,
b. is ~p ~q ∧
c. is ~p
∨
~q
So the truth table is as follows
p q p
q ∧a. q
∧
p ~p ~q b. ~p
∧
~q c. ~p
∨
~q
T T T T F F F F
T F F F F T F T
F T F F T F F T
F F F F T T T T
2. In North County, all grey dragons are predators.
a. In North County, if a dragon is grey, then he is a predator. (equivalent)
b. In North County, there exists a grey rational dragon. (negation)
c. In North County, some dragons are rational and grey. (negation)
Example of a truth table
Let p = Dragon is grey Let q = Dragon is predator
Then the bolded phrase is
∀
p, q
a. is if p then q,
