hell yeah

People gonna be talking about this one for years

Why aren't you in a book club?

parenting be like

Using these six rules and natural deduction, prove that [C > (C > C] entails C > C

Here's another one. Use any rule system you like:

1. (W ∨ X) ∨ (Y ∨ Z)
2. X → Y
3. ¬Z
∴ W v Y

A solution using a Frege-Hilbert system:

01. (W ∨ X) ∨ (Y ∨ Z)
02. X → Y
03. ¬Z
04. | ~(W v Y) - Assume
05. | ~W & ~Y - 4 DeMorgan's Theorem
06. | ~Y & ~W - 5 Commutation
07. | ~Y - 6 Simplification
08. | ~X - 2,7 Modus Tollens
09. | ~W - 5 Simplification
10. | ~W & ~ X - 8,9 Conjunction
11. | ~(W v X) - 10 DeMorgan's Theorem
12. | Y v Z - 1,11 Disjunctive Syllogism
13. | Z - 7,12 Disjunctive Syllogism
14. | Z & ~Z - 3,13 Conjunction
15. ~~(W v Y) - 4-14 Reductio ad Absurdhum/Indirect Proof
16. - W v Y - 15 Double Negation

A solution using a Fitch system:

01. (W v X) v (Y v Z)
02. X → Y
03. ¬Z
04. | ~(W v Y) - Assume
05. | | W - Assume
06. | | W v Y - 5 vI
07. | | ⊥ - 4,6 ⊥I
08. | ~W - 5-7 ~I
09. | | Y - Assume
10. | | W v Y - 9 vI
11. | | ⊥ - 4,10 ⊥I
12. | ~Y - 9-11 ~I
13. | | W v X - Assume
14. | | | W - Assume
15. | | | ⊥ - 8,14 ⊥I
16. | | | X - Assume
17. | | | Y - 2,16 →E
18. | | | ⊥ - 12,17 ⊥I
19. | | ⊥ - 13,14-15,16-18 vE
20. | | Y v Z - Assume
21. | | | Y - Assume
22. | | | ⊥ - 12,21 ⊥I
23. | | | Z - Assume
24. | | | ⊥ - 3,23 ⊥I
25. | | ⊥ - 20,21-22,23-24 vE
26. | ⊥ - 1,13-19,20-25 vE
27. ~~(W v Y) - 4-26 ~I
28. W v Y - 27 ~E

Tomorrow maybe we do FOL problems

Here's an easy set for y'all niggas:

Problem #1: ∀x(Fx → Gx), ∃xFx ⊢ ∃xGx
Problem #2: ⊢ ∀xFx v ~∀xFx
Problem #3: ∀x∀yGxy ⊢ ∃xGxx

Good morning.

Concentrate.

Problem 1: ∀x(Fx → Gx), ∃xFx ⊢ ∃xGx

Frege system:
01. ∀x(Fx → Gx)
02. ∃xFx
03. Fa - 2 Existential Instantiation
04. Fa →Ga - 1 Universal Instantiation
05. Ga - 3,4 Modus Ponens
06. ∃xGx - 5 Existential Generalization

Fitch system:
01. ∀x(Fx → Gx)
02. ∃xFx
03. | Fa - Assumption
04. | Fa →Ga - 1 ∀E
05. | Ga - 3,4 →E
06. | ∃x(Gx) - 5 ∃I
07. ∃x(Gx) - 2,3-6 ∃E

Problem #2: ⊢ ∀xFx v ~∀xFx

Frege system:
01. | ~(∀xFx v ~∀xFx) - Assume
02. | ~∀xFx & ~~∀xFx - 1, DeMorgan's Theorem
03. ~~(∀xFx v ~∀xFx) - 1-2 Indirect Proof
04. ∀xFx v ~∀xFx - Double Negation

Fitch system:
01. | ~(∀xFx ∨ ~∀xFx) - Assume
02. | | ∀xFx - Assume
03. | | ∀xFx ∨ ~∀xFx - 2 vI
04. | | ⊥ - 1,3 ⊥I
05. | ~∀xFx - 2-4 ~I
06. | ∀xFx ∨ ~∀xFx - 5 vI
07. | ⊥ - 1,6 ⊥I
08. ~~(∀xFx ∨ ~∀xFx) - 1-7 ~I
09. (∀xFx ∨ ~∀xFx) - 8 ~E

Problem #3: ∀x∀yGxy ⊢ ∃xGxx

Frege system:
01. ∀x∀yGxy
02. ∀yGay - 1 Universal Instantiation
03. Gaa - 2 Universal Instantiation
04. ∃xGxx - 3 Existential Generalization

Fitch system:
01. ∀x∀yGxy
02. ∀yGay - 1 ∀E
03. Gaa - 2 ∀E
04. ∃xGxx - 3 ∃I

Now that we've studied Frege's logic, let us move on to his social theories

Can we all chillaz

Which one of you made this form?

Very nice weather