Select the code which is not correct in the context of deductive argument with…
2016
Select the code which is not correct in the context of deductive argument with two premises :
Answer: B. An argument with two true premises and a false conclusion may be valid. — ConceptDeductive validity is a universal relation between premises and conclusion: an argument form is valid exactly when no interpretation makes every…
- A.
An argument with one true premise, one false premise and a false conclusion may be valid.
- B.
An argument with two true premises and a false conclusion may be valid.
- C.
An argument with one true premise, one false premise and a true conclusion may be valid.
- D.
An argument with two false premises and a false conclusion may be valid.
Show answer & explanation
Correct answer: B
Concept
Deductive validity is a universal relation between premises and conclusion: an argument form is valid exactly when no interpretation makes every premise true and the conclusion false. Thus the true–true–false pattern is impossible for a valid form, while each other actual truth pattern is compatible with validity if a valid form can instantiate it.
Application
Let P₁ and P₂ denote the two premises and C denote the conclusion. The true–true–false valuation makes (P₁ ∧ P₂) → C false, so it is forbidden by validity.
The statement about two true premises and a false conclusion therefore cannot describe a valid argument.
To show that the other three patterns may occur, use the valid form P ∧ Q, R ⊢ P. Whenever both premises are true, P ∧ Q itself guarantees P, so this form is valid by conjunction elimination.
Cross-check
Target premise/conclusion values | Choose P, Q, R | Values in P ∧ Q, R ⊢ P |
|---|---|---|
one true, one false ⟶ false | P=false, Q=true, R=true | false, true ⟶ false |
one true, one false ⟶ true | P=true, Q=false, R=true | false, true ⟶ true |
two false ⟶ false | P=false, Q=true, R=false | false, false ⟶ false |
Therefore, the statement that is not correct is: 'An argument with two true premises and a false conclusion may be valid.' That valuation is a counterexample to validity and cannot occur for a valid deductive form.