Ì Exam ple 8.2.12: Determine whether the following argument is valid or
not. Give the proof if it is valid.
“If today is Tuesday, then I have a test in Computer Science or a test in
Economics. If my Economics Professor is sick, then I will not have a test
in Economics. Today is Tuesday and my Economic Professor is sick.
Therefore, I have a test in Computer Science”.
Solu tion
T: Today is Tuesday
CS: I have a test in Computer Science
E: I have a test in Economics
EP: Economics Professor is sick.
( )
(
)
( )
( )
1
2
3
T
CS E
EP
E
T E
CS
→
∨
→ ¬
∧
∴
1. T
CS E
→
∨
(
)
P
2.
EP
E
→ ¬
P
3. T E
∧
P
4.
T
(3), Sim pli fi ca tion
5. CS E
∨
(1), (4), Modus Ponens
6.
E
(3), Sim pli fi ca tion
7.
¬ E
(2), (6)
8.
CS
(5), (7), Disj. Syll.
∴ The Argument is VALID.
8.3 PREDICATES AND QUANTIFIERS
Assertions which are formed using variables in a “template” that expresses the
property of an object or a relationship between objects are called “Predicates”.
Example:
(i) “He is dark and ugly” is written as
“x is dark and ugly”.
(ii) “Naveena lives in Maryland and
Menon Lakshmi lives in Texas” is written as
“x lives in Maryland and
y lives in Texas”.
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Theory of Automata, Formal Languages and Computation