![[Ch 3, 4] Logic and Proofs (2) 1. Valid and Invalid Arguments (§2.3](http://s1.studyres.com/store/data/014954007_1-d36c768aba23f0b4aa633cb9a2a27ee2-300x300.png)
[Ch 3, 4] Logic and Proofs (2) 1. Valid and Invalid Arguments (§2.3
... Example: To prove a theorem "If P(x1,..,xn), then Q (x1,..,xn)", where x1 ∈ D1,.., xn ∈ Dn. a. Direct proof and counter example o Show the theorem is true for all values of x1 ∈ D1,.., xn ∈ Dn, or show a counterexample (x1,..,xn) in which the theorem is false. o Example: Proposition: If n is any eve ...
... Example: To prove a theorem "If P(x1,..,xn), then Q (x1,..,xn)", where x1 ∈ D1,.., xn ∈ Dn. a. Direct proof and counter example o Show the theorem is true for all values of x1 ∈ D1,.., xn ∈ Dn, or show a counterexample (x1,..,xn) in which the theorem is false. o Example: Proposition: If n is any eve ...
Programming and Problem Solving with Java: Chapter 14
... A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
... A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
Conditional and Indirect Proofs
... • A tautology will follow from any premises whatever. • This is because the negation of a tautology is a contradiction, so if we use IP by assuming the negation of a tautology, we can derive a contradiction independently of other premises. This is why this process is called a zeropremise deduction. ...
... • A tautology will follow from any premises whatever. • This is because the negation of a tautology is a contradiction, so if we use IP by assuming the negation of a tautology, we can derive a contradiction independently of other premises. This is why this process is called a zeropremise deduction. ...
Show
... 4. Logic. The minor premise in a syllogism. 5. Mathematics. a. The independent variable of a function. b. The amplitude of a complex number. 6. Computer Science. A value used to evaluate a procedure or subroutine. [Middle English, from Old French, from Latin arg¿mentum, from arguere, to make clear. ...
... 4. Logic. The minor premise in a syllogism. 5. Mathematics. a. The independent variable of a function. b. The amplitude of a complex number. 6. Computer Science. A value used to evaluate a procedure or subroutine. [Middle English, from Old French, from Latin arg¿mentum, from arguere, to make clear. ...
Lecture 3 - CSE@IIT Delhi
... The final statement is called the conclusion. An argument is valid if: whenever all the assumptions are true, then the conclusion is true. If today is Wednesday, then yesterday was Tuesday. Today is Wednesday. ...
... The final statement is called the conclusion. An argument is valid if: whenever all the assumptions are true, then the conclusion is true. If today is Wednesday, then yesterday was Tuesday. Today is Wednesday. ...
Truth Tables and Deductive Reasoning
... • In fact, developments in logic over the last century have put us in a better position to say something about what it is that makes these arguments deductively valid. Indeed, we can prove that these arguments are deductively valid — that they are incapable of taking us from true premises to a false ...
... • In fact, developments in logic over the last century have put us in a better position to say something about what it is that makes these arguments deductively valid. Indeed, we can prove that these arguments are deductively valid — that they are incapable of taking us from true premises to a false ...
Logic and Reasoning
... simply do not care about children.” – “Stand back! I can help. My dad is a doctor.” – “Johnny is not fit to lead this project because he can’t even tie his shoes in the morning.” – “Mom, if you don’t buy me an iPhone, it means that you don’t really love me.” – “Would we not work harder if we made mo ...
... simply do not care about children.” – “Stand back! I can help. My dad is a doctor.” – “Johnny is not fit to lead this project because he can’t even tie his shoes in the morning.” – “Mom, if you don’t buy me an iPhone, it means that you don’t really love me.” – “Would we not work harder if we made mo ...
(˜P ∨ ˜Q) are tautologically equivalent by constructing a truth
... 2. Determine by means of truth-value analysis whether or not the following sentence is a tautology: R ↔ ((R ∨ S) ∧ (R ∨ ˜S)). ...
... 2. Determine by means of truth-value analysis whether or not the following sentence is a tautology: R ↔ ((R ∨ S) ∧ (R ∨ ˜S)). ...
writing a conclusion
... follow. Strong forces both within and without the CCP ensure that the status quo of one-party politics will remain. According to political theorist Samuel Huntington, there are three ways a country can democratize. There can be transformation of the power elites; however, the likelihood of this occu ...
... follow. Strong forces both within and without the CCP ensure that the status quo of one-party politics will remain. According to political theorist Samuel Huntington, there are three ways a country can democratize. There can be transformation of the power elites; however, the likelihood of this occu ...
Natural deduction
... – you might wonder, is this really valid? – if so, then this can be checked! try doing a truth-table. Or you can intuitively explain it to yourself like this. “Suppose that the conclusion is false. Then p ∧ q must be true while r is false. But if p ∧ q is true, then p is true. Hence p is true while ...
... – you might wonder, is this really valid? – if so, then this can be checked! try doing a truth-table. Or you can intuitively explain it to yourself like this. “Suppose that the conclusion is false. Then p ∧ q must be true while r is false. But if p ∧ q is true, then p is true. Hence p is true while ...
Rules of Inference and Methods of Proof
... of the previous ones. The body of any argument can be divided into two parts: - Premises: all but the final proposition in the argument. - Conclusion: the final proposition of the argument. So, to show the validity of any argument we show that the conclusion of the argument must follow from the trut ...
... of the previous ones. The body of any argument can be divided into two parts: - Premises: all but the final proposition in the argument. - Conclusion: the final proposition of the argument. So, to show the validity of any argument we show that the conclusion of the argument must follow from the trut ...
Fallacies of Presumption - University of Colorado Boulder
... to interpret them. This can lead us to draw erroneous conclusions from given premises. 1. Equivocation: This occurs whenever a single term is being used in two different ways within an argument. For instance: “The pamphlet for this animal rescue organization says, ‘All former zoo animals are now fre ...
... to interpret them. This can lead us to draw erroneous conclusions from given premises. 1. Equivocation: This occurs whenever a single term is being used in two different ways within an argument. For instance: “The pamphlet for this animal rescue organization says, ‘All former zoo animals are now fre ...
Homework 8 and Sample Test
... a. xy (Fxy → Fxz) b. xFxx v yFxy c. ¬x¬¬Fx d. aFa 9. “Some boys chase some girls” is best expressed in the predicate calculus by: a. xy ((Gx & By) → Cxy) b. xy ((Gx & By) & Cxy) c. xy ((Gx & By) ¬Cyx) d. xy ((Gx & By) & Cyx) 10. “Girls chase only shy boys” is best expressed in the pred ...
... a. xy (Fxy → Fxz) b. xFxx v yFxy c. ¬x¬¬Fx d. aFa 9. “Some boys chase some girls” is best expressed in the predicate calculus by: a. xy ((Gx & By) → Cxy) b. xy ((Gx & By) & Cxy) c. xy ((Gx & By) ¬Cyx) d. xy ((Gx & By) & Cyx) 10. “Girls chase only shy boys” is best expressed in the pred ...
Section 2.4: Arguments with Quantified Statements
... Thus this argument is not valid since the truth of the conclusion does not follow from the truth of the premises. Warning. When using diagrams to check for validity, make sure you consider all possible diagrams, else your proof may not be valid. 4. Inverse and Converse Errors For the last example we ...
... Thus this argument is not valid since the truth of the conclusion does not follow from the truth of the premises. Warning. When using diagrams to check for validity, make sure you consider all possible diagrams, else your proof may not be valid. 4. Inverse and Converse Errors For the last example we ...
Logic in Proofs (Valid arguments) A theorem is a hypothetical
... hypothesis, a tautology, or a consequence of previous members of the chain by using an allowable rule of inference. In creating a formal proof we use Substitution Rules Names don’t matter in a tautology (only the form)! Equivalences do not change truth value! Consider a proof of [(p 6 q) v (q 6 r) v ...
... hypothesis, a tautology, or a consequence of previous members of the chain by using an allowable rule of inference. In creating a formal proof we use Substitution Rules Names don’t matter in a tautology (only the form)! Equivalences do not change truth value! Consider a proof of [(p 6 q) v (q 6 r) v ...
Introduction to Logic
... Formal Language • Formal logic replaces the ordinary language of argument with a symbolic language. • This language is meant to be free of all ambiguity and vagueness. • The language is meant to wear its logical structure on its face. • Our formal languages: SL and QL. ...
... Formal Language • Formal logic replaces the ordinary language of argument with a symbolic language. • This language is meant to be free of all ambiguity and vagueness. • The language is meant to wear its logical structure on its face. • Our formal languages: SL and QL. ...
a. p
... Valid and Invalid Arguments Testing an Argument Form for Validity 1. Identify the premises and conclusion of the argument form. 2. Construct a truth table 3. Look at the row when all the premises are true. If the conclusion is true, it is a valid argument. Otherwise it is invalid ...
... Valid and Invalid Arguments Testing an Argument Form for Validity 1. Identify the premises and conclusion of the argument form. 2. Construct a truth table 3. Look at the row when all the premises are true. If the conclusion is true, it is a valid argument. Otherwise it is invalid ...
Quiz Game Midterm
... true, it’s valid. If there’s a row where the premises are all true but the conclusion is false, it’s invalid. ...
... true, it’s valid. If there’s a row where the premises are all true but the conclusion is false, it’s invalid. ...
logica and critical thinking
... Fallacies of relevance: When an argument relies upon premises that are not relevant to its conclusion, and therefore cannot possibly establish its truth Fallacies of weak induction: When the connection between premises and conclusion is not strong enough to support the reasoning Fallacies of presump ...
... Fallacies of relevance: When an argument relies upon premises that are not relevant to its conclusion, and therefore cannot possibly establish its truth Fallacies of weak induction: When the connection between premises and conclusion is not strong enough to support the reasoning Fallacies of presump ...
Horseshoe and Turnstiles
... is true and ψ is false, and true in all other cases. The double turnstile ‘⊧’ is the symbol for the logical implication. It expresses a (binary) relation between a premise, or a set of premises (Γ), and a conclusion (φ): Γ ⊧ φ. The relation in question can be called ‘following-from relation’ or the ...
... is true and ψ is false, and true in all other cases. The double turnstile ‘⊧’ is the symbol for the logical implication. It expresses a (binary) relation between a premise, or a set of premises (Γ), and a conclusion (φ): Γ ⊧ φ. The relation in question can be called ‘following-from relation’ or the ...
Homework #3 - Jonathan Livengood
... determine whether the argument is valid or invalid. If the TV remote isn’t working, then John has to change channels manually. John has to change channels manually. The TV remote isn’t working. 2. Translate the following argument into our formal language and then use truth tables to determine whethe ...
... determine whether the argument is valid or invalid. If the TV remote isn’t working, then John has to change channels manually. John has to change channels manually. The TV remote isn’t working. 2. Translate the following argument into our formal language and then use truth tables to determine whethe ...
1 Chapter 9: Deductive Reasoning
... Given that the validity of deductive arguments derives solely from their form, tools that enable us to examine the formal properties of deductive arguments, abstracting from the particular content of a particular argument, will be useful. Formal logical languages are such a tool. Languages in genera ...
... Given that the validity of deductive arguments derives solely from their form, tools that enable us to examine the formal properties of deductive arguments, abstracting from the particular content of a particular argument, will be useful. Formal logical languages are such a tool. Languages in genera ...
Logical Argument
... (see formal logic). Johnson and Blair (1987) define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation in everyday discourse." Opinion pieces of newspapers ...
... (see formal logic). Johnson and Blair (1987) define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation in everyday discourse." Opinion pieces of newspapers ...