Mathematical Argument

Abstract

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• A sequence of Mathematical Statement ending in a Conclusion
• Every step should follow logically from all previous steps
• IF (p AND ... p) THEN Conclusion is a [[Mathematical Statement#tautology-t|Tautology t]]
• A argument can be Valid, but if the Premise is not true, the Conclusion is going to be false

Testing An Argument Form for Valid

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• There is Critical Row in which Conclusion is false: Form is invalid
• The Conclusion in every Critical Row is true: Form is Valid

Terminologies

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Form

• The Mathematical Statement in Mathematical Argument is expressed in variables

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

Valid

• Argument Form is said to be Valid if and only if whenever Mathematical Statement substituted that make all Premise true, and the Conclusion is also true

Critical Row

• A row of Truth Table in which all the Premise are true

Sound

• A argument is called sound if & only if it is Valid & all the Premise is true