Lecture 05
Lecture 05
Lecture 05
Lecture # 05
In Today’s Lecture
Logic:
Logic rules and principles is to distinguish an argument is
valid or invalid.
Examples of Arguments:
You have a intuitive idea about argument. When you are talking
with you friend you give argument.
Sometimes you say to your friend “what are you saying has no
logic” it means you are saying that your argument is not valid.
Lawyer in court during the trail to defend client, give argument.
Judge decision is also based on lawyer argument if its argument
is valid then decision will be in his favor.
Example:
An interesting teacher keeps me awake.
I stay awake in discrete structure class.
Therefore, my discrete structure teacher is interesting.
NOTE :
The symbol read “therefore,” is normally placed just before the
conclusion.
VALID ARGUMENT
An argument is valid if the conclusion is true when all the
premises are true.
That is
Validity of argument:
When our premises conjunction is false, and conclusion is
whatever true or false, the argument is valid
When our premises conjunction is true, and conclusion is
false, then we say argument is invalid.
Argument Form
p;
q.
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Checking the validity of an argument
form
1) Construct truth table for the premises and the
conclusion;
2) Find the rows in which all the premises are true
(critical rows);
3) a. If in each critical row the conclusion
is true
then the argument form is valid;
b. If there is a row in which conclusion
is false
then the argument form is invalid.
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EXAMPLE:
Show that the following argument form is valid:
pq premise
p premise
q conclusion
premises conclusion
p q pq p q
T T T T T critical row
T F F T F
F T T F T
F F T F F
• To validity we will not analyze the whole table.
• We will analyze those rows where in premise we have T
value, and if corresponding conclusion also have T value,
then we say it’s a valid argument.
EXAMPLE OF INVALID ARGUMENT
Show that the following argument form is invalid:
pq premise
q premise
p conclusion
premises conclusion
p q pq q p
T T T T T
T F F F T critical row
F T T T F
F F T F F
pq premise
p ~q premise
pr premise
r conclusion
Is valid or invalid?
premises
conclusion
p q r p q p ~q pr r
T T T T F T T
T T F T F F F
T F T T T T T
T F F T T F F
F T T T T T T critical rows
F T F T T T F
F F T F T T T
F F F F T T F The argument is not
valid because all
corresponding values in
conclusion are not T
WORD PROBLEM
If Tariq is not on team A, then Hameed is on team B.
If Hameed is not on team B, then Tariq is on team A.
Tariq is not on team A or Hameed is not on team B.
SOLUTION:
Let
t = Tariq is on team A
h = Hameed is on team B
Then the argument is
~th
~ht
~t~h
t h ~t h ~h t ~t ~h
T T T T F
T F T T T
F T T T T
F F F F T
p q p q ~p ~q
T T T F F
T F F F T
F T T T F
F F T T T