Substitution Instances

(1) a. (1)~(X ⊃ Y) ⊃ ~(P v Q) it is a Substitution instance ____not a sub. instance

(2) ~~(P v Q)

(3) ~~ (X ⊃ Y)

b. (1) ~( F≡B) ____Substitution instance it is not a sub. instance

(2) Z⊃ (F≡B)

(3) ~Z

c. (1) (X ⊃ Y) ⊃ ~(P v Q) it is a Substitution instance _____not a sub. Instance

(2) ~~(P v Q)

(3) ~ (X ⊃ Y)

d. (1) ~(P v Q)⊃ ~Z ____Substitution instance it is not a sub. Instance

(2) Z_________

(3) ~(P v Q)

(2) a. 1) A ⊃ B ____Substitution instance it is not a sub. Instance

(2) B ⊃ X__

(3) A ⊃ X

b. (1) ~X ⊃ Y it is a Substitution instance _____not a sub. Instance

(2) Y⊃ ~M__

(3) ~X ⊃ ~M

c. (1) A ⊃ ~ B ____Substitution instance it is not a sub. Instance

(2) B ⊃ X___

(3) A ⊃ X

d. (1) ( ~ X • B) ⊃ it is a Substitution instance _____not a sub. Instance

(2) Y ⊃ ~M_

(3) ~ ( ~ X • B) ⊃ M

(3) a. (1) ~ Z v A it is a Substitution instance _____not a sub. Instance

(2) ~Z_________

(3) A

b. 1) ~(Z ≡ B) v ~ (A v B) it is a Substitution instance _____not a sub. Instance

(2) ~~ (Z≡B)_________

(3) ~(A v B)

c. (1) Z v A ____Substitution instance it is not a sub. Instance

(2) ~~Z_________

(3) A

d. 1) (Z ≡ B) v (A v B) ____Substitution instance it is not a sub. Instance

(2) ~(Z≡B)_________

(3) ~(A v B)

(4) a. (1) ~P v X it is a Substitution instance ______not a sub. Instance

(2) ~P ⊃ (B • F)

(3)Z ⊃ ~ (B • F)

(4) ~ (B • F)

b. (1) ~(P v X) it is a Substitution instance ______not a sub. Instance

(2) ~P ⊃ (B • F)

(3) ~ Z ⊃ (B • F)

(4) (B • F)

c. (1) ~P v Z it is a Substitution instance ______not a sub. Instance

(2) ~P ⊃ ~ (B • F)

(3) Z ⊃ ~ (B • F)

(4) ~ (B • F)

d. (1) (P v Z) ______Substitution instance it is not a sub. Instance

(2) P ⊃ (B v F)

(3) Z ⊃ (B • F)

(4) (B • F)

(5) a. (1) ~ (P ⊃ Z) ______Substitution instance it is not a sub. Instance

(2) ~P v (B v F)

(3) (B v F) ⊃ Y

(4) (X v Y)

b. (1)~ (P ⊃ ~X) ______Substitution instance it is not a sub. Instance

(2) (B v F) ⊃ ~Y

(3) ~ P v (B v F)

(4) ~ (X v Y)

c. 1) (P • X) it is a Substitution instance ______not a sub. Instance

(2) P⊃ X

(3) Q ⊃ Y

(4) X v Y

d. 1)~ P ⊃ ~X ______Substitution instance it is not a sub. Instance

(2) (B v F) ⊃ ~Y

(3) ~ P v (B v F)

(4) ~ X v Y

6. a. 1)~ P • Z it is a Substitution instance ______not a sub. Instance

2) ~ P

b. 1) ~(P • Q) • R ______Substitution instance it is not a sub. Instance

2) ~P • ~Q

c. 1) (~P • Q) • Z it is a Substitution instance ______not a sub. Instance

2) ~P • Q

d. 1) (P • Q) • R ______Substitution instance it is not a sub. Instance

2) P

5. Al dislikes Airedales; moreover, Bob likes beagles.

A ∧ B

6. Darla has a dachshund, yet Catherine has a Catahoula

D • C

7. Darla has a dachshund and Catherine has a Catahoula

D • C

8. Darla has a dachshund unless Al dislikes Airedales

D ⊃ ~A

9. Unless Darla has a dachshund, Bob likes beagles

B ⊃ D

10. Bob likes beagles or Al likes Airedales

B v A

11. If Bob likes beagles it is not the case that Al likes Airedales

A ⊃ ~B

12. Al likes Airedales and/or Darla has a dachshund

A v D

13. Darla has a dachshund is a sufficient condition for Al likes Airedales

D ⊃ A

14. Darla has a dachshund is a necessary condition that Al likes Airedales

D ⊃ A

15. Bob likes beagles implies that Catherine has a Catahoula

B • C

16. Bob likes beagles on the condition that Al likes Airedales

B ⊃ A

17. If Bob likes beagles then Bob likes beagles

B ⊃ B

18. Catherine has a Catahoula only if AI likes Airedales

C ⊃ A

19. Darla has a dachshund given Al likes Airedales

D ⊃ A

20. Provided Al likes Airedales, Bob likes beagles

B ⊃ A

21. Catherine has a Catahoula if and only if Bob likes beagles

C ⊃ C

22. Bob likes beagles if Darla has a dachshund

B ⊃ D

23. Al likes Airedales or Bob doesn’t like beagles

A v ~B

24. Al likes Airedales or Al doesn’t like Airedales

A v ~A

25. Al likes Airedales just in case Bob doesn’t like beagles

A? ~B