Inference Basics sample questions

Question: Given the pair of statements: G ⊃ (W ∨ ~Q) and (W ∨ ~G) • ~(Q • G) These statements are:

Answer Choices: a. Inconsistent b. Contradictory c. Invalid d. Logically equivalent e. Consistent

Answer: a. Inconsistent

Question: Given the pair of statements: P • ~Z and Z ≡ P

Answer Choices: a. Inconsistent b. Valid c. Contradictory d. Consistent e. Logically equivalent

Answer: a. Inconsistent

Question: Given the argument: M ⊃ J / ~J ∨ R // (M ∨ ~R) ⊃ J

Answer Choices: a. Invalid: fails in 3rd line b. Invalid: fails in 2nd line c. Invalid: fails in 4th line d. Invalid: fails in 1st line e. Valid

Answer: e. Valid

Question: Given the argument: Q ⊃ A / ~A ∨ Q / A ≡ Q

Answer Choices: a. Invalid; fails in 1st line b. Valid c. Invalid; fails in 3rd line d. Invalid; fails in 2nd line e. Invalid; fails in 4th line

Answer: c. Invalid; fails in 3rd line

Question: Given the argument: R ⊃ (H • ~N) / (H • ~B) ⊃ (N ∨ ~P) / K ⊃ (G • P) // (K • R) ⊃ B

Answer Choices: a. Invalid b. Valid c. Uncogent d. Cogent e. Sound

Answer: b. Valid

Question: Given the argument: S ⊃ W / C ⊃ L / (M • ~L) ∨ (D • ~W) / C ∨ S // D • M

Answer Choices: a. Invalid b. Cogent c. Sound d. Valid e. Uncogent

Answer: a. Invalid

Question: Given the statements: H ⊃ E / M ⊃ R / (M • E) ⊃ G / (R • G) ⊃ E / M ∨ E

Answer Choices: a. Invalid b. Tautologous c. Consistent d. Logically equivalent e. Inconsistent

Answer: c. Consistent

Question: Given the statements: C ⊃ L / K ⊃ ~H / L ⊃ (N ⊃ K) / C ⊃ (H ⊃ N) / C • H

Answer Choices: a. Contradictory b. Tautologous c. Consistent d. Inconsistent e. Valid

Answer: d. Inconsistent

Question: B ⊃ ~Q~Q∴ ~B

Answer Choices: a. Modus ponens b. Modus tollens c. Disjunctive syllogism d. Invalid e. Denying the antecedent

Answer: b. Modus tollens

Question: (-N ⊃ R) • (F ⊃ ~G)F ∨ ~N∴ R ∨ ~G

Answer Choices: a. Constructive dilemma b. Invalid c. Denying the antecedent d. Modus tollens e. Destructive dilemma

Answer: e. Destructive dilemma

Question: ~H ⊃ ~B K ⊃ ~H K ⊃ ~B

Answer Choices: a. Denying the antecedent b. Invalid c. Pure hypothetical syllogism d. Constructive dilemma e. Destructive dilemma

Answer: c. Pure hypothetical syllogism

Question: D ⊃ ~N ~N ∴ D

Answer Choices: a. Affirming the consequent b. Invalid c. Denying the antecedent d. Modus ponens e. Modus tollens

Answer: a. Affirming the consequent

Question: S ⊃ ~R N ⊃ R S ⊃ N

Answer Choices: a. Disjunctive syllogism b. Constructive dilemma c. Pure hypothetical syllogism d. Affirming the consequent e. Invalid

Answer: e. Invalid

Question: ~P ∨ M P ∴ M

Answer Choices: a. Modus tollens b. Denying the antecedent c. Pure hypothetical syllogism d. Disjunctive syllogism e. Invalid

Answer: d. Disjunctive syllogism

Question: ~L ⊃ F L ∴ F

Answer Choices: a. Disjunctive syllogism b. Denying the antecedent c. Modus tollens d. Modus ponens e. Invalid

Answer: d. Modus ponens

Question: ~G ⊃ A ~G ∴ A

Answer Choices: a. Constructive dilemma b. Disjunctive syllogism c. Modus ponens d. Denying the antecedent e. Invalid

Answer: c. Modus ponens

Question: G ∨ ~T ~T ∴ G

Answer Choices: a. Invalid b. Disjunctive syllogism c. Modus ponens d. Affirming the consequent e. Modus tollens

Answer: a. Invalid