Dr. Byrne
Spring 2009
Math 110
Section 1.2
Worksheet on Symbolic Logic
1. From words to symbols.
Using the symbolic representations p and q, express the following compound statements
in symbolic form.
p: The food is spicy.
q: The food is aromatic.
a. The food is aromatic and spicy.
b. If the food isn’t spicy, it isn’t aromatic.
c. The food is spicy and it isn’t aromatic.
d. The food isn’t spicy or aromatic.
In Symbols
_________
_________
_________
_________
2. From symbols to words.
Using the symbolic representations p and q, express the following in words.
p: I am an environmentalist.
q: I recycle my aluminum cans.
In Words
a. ~p
b. ~q
c. p^q
d. pq
e. ~q~p
f. q  ~p
3. From words to symbols when the symbols are not provided.
Express the following compound statement in symbolic form.
If I jump off the bridge, I will break my leg or I’ll be fine.
(First, break up the compound statement into simple statements and assign symbols to the
simple statements. Then you can write the compound statement symbolically.)
4. Translating Ordinary Language Into Symbolic Notation
Human language is complex, context-dependent, flexible and evolving. Symbolic
notation can be thought of as an artificial, simplified language to avoid (and explore!) the
difficulties of vagueness (incomplete meaning), equivocation (multiple meaning due to
context), and amphiboly (multiple meaning due to sentence structure) of ordinary
language.
The qualifier ‘all’
All red cars go 140 mph.
q: The car goes 140 mph.
r: The car is red.
How do we translate the meaning of this sentence in symbols?
First, rephrase: __________________________________________________________
In symbols: ____________
 When you see the qualifier, “all”, you need to rephrase the sentence with an “if..then”
The qualifier ‘no’
No person that is a convicted felon is
eligible to vote.
q: A person is a convicted felon.
r: A person is eligible to vote.
How do we translate the meaning of this sentence in symbols?
First, rephrase: __________________________________________________________
In symbols: ____________
5. Symbolic notation when the symbols are not given and there is a missing subject.
“All squares are rectangles.”
Translate the sentence into symbolic form, defining each letter you use.
The problem: What is being a square? What is the subject?
The solution: Create a subject! For this class, the more inventive, the better.
Solution 1:
Solution 2:
Rephrase as, “If it is a square, then it is a rectangle.”
p=It is a square.
q=It is a rectangle.
In symbols, the statement is: _______________