Section 2.7 Self Quiz

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(A ∨ B) ⊃ C
C ⊃ ~D / D ⊃ A

Valid

Invalid. Counterexample when B, C, and D are true and A is false

Invalid. Counterexample when B and D are true and A and C are false

Invalid. Counterexample when C and D are true and A and B are false

Invalid. Counterexample when A, B, and C are false and D is true

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
E ⊃ F
G ⊃ ~F / ~G ∨ ~E

Valid

Invalid. Counterexample when E, F, and G are true

Invalid. Counterexample when E and G are true and F is false

Invalid. Counterexample when F and G are true and E is false

Invalid. Counterexample when E and F are true and G is false

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
H ≡ (~I ∨ J)
H ∨ ~J / ~I

Valid

Invalid. Counterexample when H, I, and J are false

Invalid. Counterexample when H and I are true and J is false

Invalid. Counterexample when I and J are true and H is false

Invalid. Counterexample when I is true and H and J are false

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(K · L) ⊃ M
N ⊃ ~M
N ∨ K / L ⊃ K

Valid

Invalid. Counterexample when L, M, and N are true and K is false

Invalid. Counterexample when L and M are true and K and N are false

Invalid. Counterexample when L and N are true and K and M are false

Invalid. Counterexample when L is true and K, M, and N are false

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
P ⊃ (Q ∨ R)
(Q · S) ⊃ ~P
~(~Q ∨ R) / ~P

Valid

Invalid. Counterexample when P, Q, R, and S are true

Invalid. Counterexample when P and Q are true and R and S are false

Invalid. Counterexample when P, R, and S are true and Q is false

Invalid. Counterexample when P and S are true and Q and R are false

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(T · ~U) ⊃ ~W
~W ⊃ X
~Z ⊃ W
~(X · Z) / T ⊃ U

Valid

Invalid. Counterexample when T, X, and Z are true and U and W are false

Invalid. Counterexample when T and X are true and U, W, and Z are false

Invalid. Counterexample when T, W, and Z are true and U and X are false

Invalid. Counterexample when T and W are true and W, X, and Z are false

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
A ⊃ (~B ≡ C)
B ≡ D
~C ≡ ~D / ~A

Valid

Invalid. Counterexample when A, B, and D are true and C is false

Invalid. Counterexample when A and B are true and C and D are false

Invalid. Counterexample when A, C, and D are true and B is false

Invalid. Counterexample when A and C are true and B and D are false

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
E ⊃ (F ∨ ~G)
F ⊃ (~E ∨ ~G) / ~(E ≡ F)

Valid

Invalid. Counterexample when E, F, and G are true

Invalid. Counterexample when E and F are true and G is false

Invalid. Counterexample when E, F, and G are false

Invalid. Counterexample when F is true and E and G are false

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
H ≡ (I · ~J)
K ≡ ~H
~(K ⊃ J) / I ≡ J

Valid

Invalid. Counterexample when I, H, and K are true and J is false

Invalid. Counterexample when I and H are true and J and K are false

Invalid. Counterexample when K is true and I, H, and J are false

Invalid. Counterexample when J is true and H, I and K are false

. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
L ⊃ [(M ∨ ~N) ⊃ O]
(N ⊃ O) ⊃ (~P ⊃ Q)
R ⊃ ~Q / L ⊃ (R ⊃ P)

Valid

Invalid. Counterexample when L, M, O, Q, and R are true and N and P are false

Invalid. Counterexample when L, N, O, Q, and R are true and M and P are false

Invalid. Counterexample when L, M, N, O, and R are true and P and Q are false

Invalid. Counterexample when L, N, and R are true and M, O, P, and Q are false

. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
(A ∨ B) ∨ C
~C
~A ⊃ B

Inconsistent

Consistent. Consistent valuation when A and B are true and C is false

Consistent. Consistent valuation when A and C are true and B is false

Consistent. Consistent valuation when B and C are true and A is false

Consistent. Consistent valuation when A, B, and C are false

. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
D ≡ E
F ∨ D
~E · ~F

Inconsistent

Consistent. Consistent valuation when D, E, and F are true

Consistent. Consistent valuation when D and E are true and F is false

Consistent. Consistent valuation when D and F are true and E is false

Consistent. Consistent valuation when D, E, and F are false

. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
(G ≡ H) ⊃ H
~H ∨ I
G · ~I

Inconsistent

Consistent. Consistent valuation when G, H, and I are true

Consistent. Consistent valuation when G and H are true and I is false

Consistent. Consistent valuation when G and I are true and H is false

Consistent. Consistent valuation when G is true and H and I are false

. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
~(J ∨ ~K)
L ⊃ M
(J ∨ L) ⊃ (K · M)

Inconsistent

Consistent. Consistent valuation when J, K, and M are true and L is false

Consistent. Consistent valuation when L and M are true and J and K are false

Consistent. Consistent valuation when K and M are true and J and L are false

Consistent. Consistent valuation when K and L are true and J and M are false

. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
~N ≡ (O · P)
~O ⊃ Q
N · ~Q

Inconsistent

Consistent. Consistent valuation when N, O, and P are true and Q is false

Consistent. Consistent valuation when N and O are true and P and Q are false

Consistent. Consistent valuation when N and P are true and O and Q are false

Consistent. Consistent valuation when N, O, and Q are true and P is false

. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
P ≡ Q
~Q ≡ R
R ≡ P
S ≡ ~P
S ≡ R

Inconsistent

Consistent. Consistent valuation when P and Q are true and R and S are false

Consistent. Consistent valuation when P, Q, R, and S are true

Consistent. Consistent valuation when R and S are true and P and Q are false

Consistent. Consistent valuation when P, Q, R, and S are false

. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
(T ⊃ U) ⊃ (W ⊃ U)
T ⊃ ~(U ⊃ X)
(T ⊃ ~X) ⊃ W

Inconsistent

Consistent. Consistent valuation when U, W, and X are true and T is false

Consistent. Consistent valuation when W and X are true and T and U are false

Consistent. Consistent valuation when T and U are true and W and X are false

Consistent. Consistent valuation when T and W are true and U and X are false

. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
A ⊃ (~B ∨ C)
C ⊃ D
A ∨ (B · ~D)
A ≡ (B ⊃ D)

Inconsistent

Consistent. Consistent valuation when A and D are true and B and C are false

Consistent. Consistent valuation when A, B, and D are true and C is false

Consistent. Consistent valuation when C and D are true and A and B are false

Consistent. Consistent valuation when B and C are true and A and D are false

. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
(E ⊃ F) ⊃ G
(~E ∨ F) ≡ (H ∨ I)
I ⊃ (J ⊃ ~H)
~G ⊃ ~J

Inconsistent

Consistent. Consistent valuation when E is true and F, G, H, I, and J are false

Consistent. Consistent valuation when E and H are true and F, G, I, and J are false

Consistent. Consistent valuation when E and I are true and F, G, H, and J are false

Consistent. Consistent valuation when F, G, H, I, and J are true and E is false

Quiz Content