Abstract
- A sequence of Premise ending in a Conclusion
- Every step should follow logically from all previous steps
IF (p AND ... p) THEN Conclusionis a Tautology- An argument can be Valid, but if the Premise is not true, the Conclusion is going to be false
Premise
- Also known as Assumption or Hypothesis
- A Mathematical Statement
Conclusion
- A Mathematical Statement that must be true when all Premise are true, in order for the Mathematical Argument to be Valid
Validity
Critical Row
- A row of Truth Table in which all the Premise are true
Valid
- Does the conclusion follow logically from the premises, regardless of whether those premises are actually true?
- Mathematical Argument is said to be Valid if and only if whenever Mathematical Statement substituted that make all Premise true, and the Conclusion is also true
- The conclusion logically follows from the premises. It doesn’t guarantee that the premises themselves are actually true.
Important
There is Critical Row in which Conclusion is false: invalid.
The Conclusion in every Critical Row is true: valid.
For all non-critical rows, regardless is conclusion is true or false: valid.
Sound
- A Mathematical Argument is called sound if & only if it is Valid AND all the Premise is true. That means the Conclusion also must be true