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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
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