This document discusses arguments and their validity. It defines arguments as statements with premises and a conclusion. Valid arguments are those where the conclusion logically follows from the premises. Invalid arguments have conclusions that can be false even when the premises are true. The document provides examples of valid and invalid arguments. It also discusses rules of inference like modus ponens and modus tollens that are used to determine validity.

1. ‫يم‬ ِ‫ح‬َّ‫الر‬ ِ‫ن‬ ٰ‫حم‬َّ‫الر‬ ِ‫ہللا‬ ِ‫سم‬ِ‫ب‬

2. 1 Arguments 2 Valid Arguments
C O N T E N T S
3 Invalid Arguments
Zofshan CS-79
Muqadas Javaid CS-76
Shaharmeer CS-2822
P R E S E N T E D B Y

3. 01
Arguments

4. 1 Arguments
Arguments:
The arguments can be described as a series of statements or
propositions. It usually has the premises and conclusion.
 Permises:
All the statement or proposition in an argument is called
premises (or assumption or hypotheses) Expect for the final one.
The premises will be represented by p1, p2, p3,....,pn.
 Conclusion:
The final statement is called conclusion.
Statement is supported by atleast one permise.
The symbol (...),which is read “therefore,” is normally
placed just before the conlusion.

5. 1 Arguments
Examples 1:
“If you have a current password ,then you can login into the network.”
If you have a current password, then you can login into the network.
You have a current password.
Therefore, you can login into the network.
If p, then q. p → q
p. p
Therefore,q. ...q
P1, P2, ..., Pn → Q
Where P1, P2...... Pn is the premises
and Q is the conclusion.

6. 1 Arguments
Examples 2:
Every student of conputer science studies Dicrete Structures.
Data structures necessarily contain the study of arguments.
Therefore, every student of computer sciece studies
arguments.
Examples 3:
Every parent is a mature person.
Children should listen to mature people.
Therefore, every child should listen to their parents.

7. 1 Arguments
Rules Of Inference:
 The rules of inference are a logical form or guide consisting
of premises (or hypotheses) and draws a conclusion.
 Rules of inference are the tamplates for constructing valid
arguments.
 Deriving conclusion from the evidences.
 The general form of the rule of inference is:
(p1^p2^....^pn)→ c

8. 1 Arguments
Types Rules Of Inference:
1. Modus Ponens: p→q
p OR [(p→ q)^q]→q
...q
P1 If p, then q.
P2 p.
C Therefore,q.
Example:
If it rain, then it is cloudy.
It rains.
Therefore, it is cloudy.

9. 1 Arguments
Modus Ponens :
p q p→q (p→ q)^q [(p→q)^q]→q
T T T T T
T F F F T
F T T F T
F F T F T

10. 1 Arguments
Types Rules Of Inference:
1. Modus Tollens: p→q
~q OR [(p→ q)^~q]→~p
...~p
P1 If p, then q.
P2 ~q.
C Therefore,~p.
Example:
If it rainI am the POTUS , then i’m an American citizen.
I’m not an American citizen.
Therefore, i’m not the POTUS.

11. 1 Arguments
Modus Tollens :
p q p→q ~p ~q (p→ q)^~q [(p→q)^~q]→~p
T T T F F F T
T F F F T F T
F T T T F F T
F F T T T T T

12. 1 Arguments
Uses And Application:
 Arguments are used in computer programming.
 Arguments are used in critical thinking.
 Arguments are used to test logical ability.
 Arguments offer proof for a claim or conclusion.
 Argument mapping is useful in philosophy, management reporting,
military, and intelligence analysis, and public debates.

13. 03
Invalid Arguments

14. Invalid Arguments
An argument is said to be an invalid argument if
its conclusion can be false when its hypothesis
is true.
The main point regarding a valid argument is that it follows from the logical form
itself and has nothing to do with the content. When a conclusion is reached
using a valid argument

15. How to Check If an Argument is Invalid?

16. 3 Invalid Arguments
To test whether or not an argument is invalid, we have to:
Identify premises and conclusion
Construct a truth table showing conclusion
Look for all the rows where the premises are all true - (critical
rows)
If the conclusion is false in a critical row,
then the argument is invalid.
Otherwise, the argument is valid
2.
3.
1.

17. Invalid Arguments
In logic, the words “false” and “invalid” have
very different meanings
- false is talking about the statements
making up an argument
- invalidity is talking about whether the
conclusion follows from the premises or
not.
3
Warning

18. Invalid Arguments
- A perfectly valid argument may have a false
conclusion depending upon the truth value of
the premises.
- An invalid argument may have a true
conclusion depending upon the truth value of
the premises.
3
Note

19. Examples

20. Invalid Arguments
3
Let us consider the following example:
Egyptions speak Arabic.
It can be rewritten as
“If someone is a citizen of Egypt, then they speak Arabic.”
(p→q) → (q→p)
Arguments
(p→q) V (q→p)

21. Invalid Arguments
3
An example of an invalid argument :
“If it is raining, then the streets are wet.
The streets are wet.
Therefore, it is raining.”
For convenience, we will represent this argument
symbolically as
[ ( p → q ) ∧ p ] → p
1.

22. Invalid Arguments
3
p q p→q (p→q)∧p [(p→q)∧p]→p
T T T T T
T F F F T
F T T F T
F F T F T

23. Invalid Arguments
3
p q p→q ~p ~q (p→q)∧∼p [(p→q)^~p]→~q
T T T F F F T
T F F F T F T
F T T T F T F
F F T T T T T
[ ( p → q ) ^ ~ p ] → ~ q
2.

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