PHI 1010Homework 12 - Exercise 7.4 All--VERIFIED BY EXPERTS-ALL ANSWERS CORRECT

Homework 12: Exercise 7.4 All Exercise 7.4A Problem 1 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter A is assigned F, B is assigned T, and C is assigned F, so you have shown that the argument is invalid! Your truth table: A B C | A → (B → C) ∴ B → C ------|------------------------ FTF | FTTFFTFF Exercise 7.4A Problem 2 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter E is assigned F and F is assigned T, so you have shown that the argument is invalid! Your truth table: E F | ~(E ↔ F) ∴ ~E ∙ ~F ----|---------------------- FT |TFFTTFFFT Exercise 7.4A Problem 3 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter G is assigned F and H is assigned T, so you have shown that the argument is invalid! Your truth table: G H | ~(G ↔ H) ∴ ~G → ~H ----|----------------------- FT | TFFTTFFFTExercise 7.4A Problem 4 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter J is assigned F and K is assigned F, so you have shown that the argument is invalid! Your truth table: J K | J → ~K ∴ ~(J ↔ K) ----|---------------------- FF| FTTFFFTF Exercise 7.4A Problem 5 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter P is assigned T, Q is assigned F, and R is assigned F, so you have shown that the argument is invalid! Your truth table: P Q R | (P ∙ Q) → R, ~R ∴ ~P ------|----------------------- T F F | T F F T F TF FT Exercise 7.4A Problem 6 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter Z is assigned T, H is assigned F, Y is assigned F, and W is assigned F, so you have shown that the argument is invalid! Your truth table: Z H Y W | ~(Z ∙ H), ~Z → Y, W → H ∴ ~W → Y --------|------------------------------------- T F F F |T T F F F T T F F T F T F F F Exercise 7.4A Problem 7Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter S is assigned F, H is assigned T, and U is assigned T, so you have shown that the argument is invalid! Your truth table: S H U | ~(S ∙ H), (~S ∙ ~H) → ~U ∴ ~U ------|-------------------------------- FTT | TFFTTFFFTTFTFT Exercise 7.4A Problem 8 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter F is assigned F, G is assigned T, and H is assigned F, so you have shown that the argument is invalid! Your truth table: F G H | (F ∙ G) ↔ H, ~H ∴ ~G ------|------------------------ F T F | F F T T F TF FT Exercise 7.4A Problem 9 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter B is assigned T, C is assigned F, D is assigned T, and E is assigned T, so you have shown that the argument is invalid! Your truth table: B C D E | ~(B → C), (D ∙ C) ∨ E ∴ ~B --------|----------------------------- TFTT | TTFFTFFTTFT Exercise 7.4A Problem 10Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter P is assigned T, Q is assigned T, and R is assigned T, so you have shown that the argument is invalid! Your truth table: P Q R | (P → ~Q) ↔ ~R, R ∴ ~P ------|-------------------------- TTT | TFFTTFTTFT Exercise 7.4A Problem 11 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter S is assigned F, T is assigned F, and V is assigned F, so you have shown that the argument is invalid! Your truth table: S T V | S → (T → V) ∴ (S → T) → V ------|------------------------------- FFF | FTFTFFTFFF Exercise 7.4A Problem 12 Correct! Argument is invalid! Your abbreviated truth table is correct! Row 1 shows that the premises are all true and the conclusion is false when statement letter A is assigned T, B is assigned F, and C is assigned T, so you have shown that the argument is invalid! Your truth table: A B C | A → (B → C) ∴ A → (B ∙ C)