Section 3.07 Self Quiz

. Consider assuming 'G' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. G ⊃ H
2. G ⊃ I

H

I

H • I

Options A, B, and C

Options A and B, but not option C

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. G ⊃ H
2. G ⊃ I

G ≡ H

G ≡ (H • I)

G ⊃ (H • I)

All of the above

None of the above

. Consider assuming 'J' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. J ⊃ K
2. ~J ∨ L
3. (K • L) ≡ M

K

~K

~L

L ⊃ J

None of the above

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. J ⊃ K
2. ~J ∨ L
3. (K • L) ≡ M

J ⊃ ~K

J ⊃ ~L

J ⊃ M

M ⊃ J

None of the above

. Consider assuming 'N ∨ P' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. ~(N ∨ O)
2. P ⊃ ~Q

~N ∨ ~O

~N • ~O

~N

~Q ⊃ P

O ∨ Q

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. ~(N ∨ O)
2. P ⊃ ~Q

(N ∨ P) ⊃ O

(N ∨ P) ⊃ (O • P)

(N ∨ P) • (Q ∨ R)

(N ∨ P) ⊃ ~(O ∨ Q)

(M ∨ P) ⊃ R

. Consider assuming 'S' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. ~R ≡ S
2. T ⊃ R
3. ~(R ∨ T) ⊃ U

R ≡ ~S

S ≡ R

~S ≡ ~ R

S ≡ ~R

S ⊃ ~R

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. ~R ≡ S
2. T ⊃ R
3. ~(R ∨ T) ⊃ U

S ⊃ R

S ⊃ T

S ⊃ (R • T)

S ⊃ U

S ⊃ (R • U)

. Consider assuming 'A' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. A ⊃ (B ∨ C)
2. ~A ∨ (D ∨ E)
3. ~(C ∨ E)

B ∨ C

~~A

~C • ~E

All of the above

Options A and B, but not option C

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. A ⊃ (B ∨ C)
2. ~A ∨ (D ∨ E)
3. ~(C ∨ E)

A ⊃ C

A ⊃ E

A ⊃ (B • C)

A ⊃ (D • E)

A ⊃ (B • D)

. Consider assuming 'F' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. F ⊃ [(G ∨ H) ⊃ I]

G ∨ H

(G ∨ H) ⊃ I

[F • (G ∨ H)] ⊃ I

All of the above

Options B and C, but not option A

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. F ⊃ [(G ∨ H) ⊃ I]

F ⊃ I

F ⊃ (G ⊃ I)

(F ⊃ G) ⊃ I

[F ⊃ (G ∨ H)] ⊃ I

I ⊃ F

. Consider assuming 'J' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. J ⊃ (K ⊃ M)
2. L ∨ ~M
3. J ∨ (K • ~L)

K ⊃ M

K

M

K • ~L

~L

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. J ⊃ (K ⊃ M)
2. L ∨ ~M
3. J ∨ (K • ~L)

J ≡ K

J ≡ (K ⊃ L)

J ≡ L

J ≡ M

J ≡ (M ⊃ L)

. Consider assuming '~P' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. (N ⊃ O) ⊃ P
2. (~N ∨ O) ≡ (~Q ⊃ R)
3. R ∨ (S ⊃ Q)

(N ⊃ O) ≡ (~Q ⊃ R)

(~N ⊃ O) ≡ (~Q ⊃ R)

(~N ∨ O) ≡ (R ⊃ ~Q)

(~N ∨ O) ≡ (~~Q ⊃ ~R)

(O ⊃ ~N) ≡ (~Q ⊃ R)

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. (N ⊃ O) ⊃ P
2. (~N ∨ O) ≡ (~Q ⊃ R)
3. R ∨ (S ⊃ Q)

~P ⊃ ~N

~P ⊃ O

~P ⊃ Q

~P ⊃ ~R

~P ⊃ ~S

. Consider assuming '~X' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. X ⊃ (~Y ∨ Z)
2. ~X ⊃ (Y ∨ Z)
3. ~Z

~(~Y ∨ Z)

(~Y ∨ Z)

(Y ∨ Z)

~(Y ∨ Z)

~X ≡ ~Z

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. X ⊃ (~Y ∨ Z)
2. ~X ⊃ (Y ∨ Z)
3. ~Z

X ≡ Z

X ≡ ~Z

Z ≡ ~X

X ≡ Y

X ≡ ~Y

. Consider assuming 'B' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
1. A ≡ ~(B ∨ C)
2. ~D ≡ (A • E)
3. (D ⊃ B) • (E ⊃ B)

D

~D

E

~E

B ∨ C

. Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
1. A ≡ ~(B ∨ C)
2. ~D ≡ (A • E)
3. (D ⊃ B) • (E ⊃ B)

B ≡ D

B ≡ E

B ≡ (D ∨ E)

B ≡ A

B ≡ (A ∨ E)

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