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Discrete Structure

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Syed Umair
Syed Umair

1. An argument consists of premises followed by a conclusion. The validity of an argument depends on whether the conclusion is true if all the premises are true. 2. To determine if an argument form is valid or invalid, a truth table is constructed showing the truth values of the premises and conclusion. If there is a "critical row" where all premises are true but the conclusion is false, then the argument form is invalid. 3. This particular argument is invalid because there is at least one critical row where the premises are all true but the conclusion is false.

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Argument 1 Assignment No.1 Submitted To: Sir Adnan Nawaz Submitted By: Syed Muhammad Umair Shah Subject: Discrete Structure Department: Computer Science Semester: 2nd Roll No. 12 Indus International Institute D.G.Khan
Argument 2 ARGUMENT An argument is a list of statements is called premisesor (Assumptions / Hypotheses)followed by a statement is called the conclusion. An argument is a sequence of statements, and an argument form is a sequence of statement forms.All statements in an argument form, exceptfor the final one, are called premises (or assumptions or hypotheses).The final statement or statement form is called the conclusion To say that an argument form is valid means that no matter what particular statements are substituted for the statement variables in its premises,if the resulting premises are all true, then the conclusionis also true. To say that an argument is valid means that its form is valid. P1 Premise P2 Premise P3 Premises ..P n Premise C Conclusion NOTE: this symbol is normally placed just before the conclusion. This symbol is normally read therefore, Determining Validity or Invalidity Determine whether the following argument form is valid or invalid by drawing a truth table, indicating which columns representthe premises and which representthe conclusion, and annotating the table with a sentence of explanation. When you fill in the table, you only need to indicate the truth values for the conclusion in the rows where all the premises are true (the
Argument 3 critical rows) because the truth values of the conclusionin the other rows are irrelevant to the validity of invalidity of the argument VALID AND INVALID ARGUMENT: An argument is valid when all the premises are true and also the conclusionis true. Alternatively, an argument is valid if conjunction of its premises imply conclusion.Also rememberthat an argument is valid if in all critical rows conclusionhas truth value T That is (P1 P2 P3 . . . P n) C is a tautology. An argument is invalid if the conclusionis false when all the premises are true. Alternatively, an argument is invalid if conjunction of its premises does not imply conclusion. Testing an Argument Form for Validity 1. Identifythe premises and conclusionof the argument form. 2. Construct a truth table showing the truth values of all the premises and the conclusion. 3. A row of the truth table in which all the premises are true is called a critical row. If there is a critical row in which the conclusion is false, then it is possibleforan argument of the given form to have true premises and a false conclusion,and so the argument form is invalid. If the conclusionin every critical row is true, then the argument form is valid.
Argument 4 This argument is Valid because in this argument all premises and conclusionhave truth value T .When all premises and conclusion are true then make a valid argument CRITICAL ROWS: When all premises are true then that row is called critical row, if conclusion is false then also makes a critical row This argument is Invalid because all premises have truth value T. But in conclusionColum has Truth value F so this argument is Invalid.
Argument 5 This argument is Invalid because in this argument has three critical rows in which two critical rows has all truth value T, but in 3rd row in conclusion Colum one value is false so this argument is Invalid.
Argument 6 This Argument is invalid. Because there are three critical rows the critical rows are those rows where the premiseshave truth value T. And in the first critical row conclusion has truth value F. so we say that this argument is invalid.
Argument 7 This argument is Invalid because there have two critical rows 1st critical row conclusionhas Truth value F, so this argument is Invalid.
Argument 8 This argument is valid. Because there are five critical rows .That the critical rows are those rows where the premiseshave truth value T, and in all critical row conclusions have truth value T. so we say that this argument is valid because all critical rows conclusionhas truth value T.
Argument 9 This argument is invalid because,there have two critical rows. 2nd critical conclusionrow have truth value F, so this argument is Invalid.

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Discrete Structure

  • 1. Argument 1 Assignment No.1 Submitted To: Sir Adnan Nawaz Submitted By: Syed Muhammad Umair Shah Subject: Discrete Structure Department: Computer Science Semester: 2nd Roll No. 12 Indus International Institute D.G.Khan
  • 2. Argument 2 ARGUMENT An argument is a list of statements is called premisesor (Assumptions / Hypotheses)followed by a statement is called the conclusion. An argument is a sequence of statements, and an argument form is a sequence of statement forms.All statements in an argument form, exceptfor the final one, are called premises (or assumptions or hypotheses).The final statement or statement form is called the conclusion To say that an argument form is valid means that no matter what particular statements are substituted for the statement variables in its premises,if the resulting premises are all true, then the conclusionis also true. To say that an argument is valid means that its form is valid. P1 Premise P2 Premise P3 Premises ..P n Premise C Conclusion NOTE: this symbol is normally placed just before the conclusion. This symbol is normally read therefore, Determining Validity or Invalidity Determine whether the following argument form is valid or invalid by drawing a truth table, indicating which columns representthe premises and which representthe conclusion, and annotating the table with a sentence of explanation. When you fill in the table, you only need to indicate the truth values for the conclusion in the rows where all the premises are true (the
  • 3. Argument 3 critical rows) because the truth values of the conclusionin the other rows are irrelevant to the validity of invalidity of the argument VALID AND INVALID ARGUMENT: An argument is valid when all the premises are true and also the conclusionis true. Alternatively, an argument is valid if conjunction of its premises imply conclusion.Also rememberthat an argument is valid if in all critical rows conclusionhas truth value T That is (P1 P2 P3 . . . P n) C is a tautology. An argument is invalid if the conclusionis false when all the premises are true. Alternatively, an argument is invalid if conjunction of its premises does not imply conclusion. Testing an Argument Form for Validity 1. Identifythe premises and conclusionof the argument form. 2. Construct a truth table showing the truth values of all the premises and the conclusion. 3. A row of the truth table in which all the premises are true is called a critical row. If there is a critical row in which the conclusion is false, then it is possibleforan argument of the given form to have true premises and a false conclusion,and so the argument form is invalid. If the conclusionin every critical row is true, then the argument form is valid.
  • 4. Argument 4 This argument is Valid because in this argument all premises and conclusionhave truth value T .When all premises and conclusion are true then make a valid argument CRITICAL ROWS: When all premises are true then that row is called critical row, if conclusion is false then also makes a critical row This argument is Invalid because all premises have truth value T. But in conclusionColum has Truth value F so this argument is Invalid.
  • 5. Argument 5 This argument is Invalid because in this argument has three critical rows in which two critical rows has all truth value T, but in 3rd row in conclusion Colum one value is false so this argument is Invalid.
  • 6. Argument 6 This Argument is invalid. Because there are three critical rows the critical rows are those rows where the premiseshave truth value T. And in the first critical row conclusion has truth value F. so we say that this argument is invalid.
  • 7. Argument 7 This argument is Invalid because there have two critical rows 1st critical row conclusionhas Truth value F, so this argument is Invalid.
  • 8. Argument 8 This argument is valid. Because there are five critical rows .That the critical rows are those rows where the premiseshave truth value T, and in all critical row conclusions have truth value T. so we say that this argument is valid because all critical rows conclusionhas truth value T.
  • 9. Argument 9 This argument is invalid because,there have two critical rows. 2nd critical conclusionrow have truth value F, so this argument is Invalid.