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!
You...
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PHI 1010 Logic
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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
----|-----------------------
F T | T F F T TF F FT
, Exercise 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)
----|----------------------
F F | F T TF F F T F
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 7
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, 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
------|--------------------------------
F T T | T F F T TF F FT T FT FT
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 10
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