Logic/Logic patterns

A: a, b, 0, 1, +, -, ., /, =, =/=, ~,.

B: ++ = +, +- = +-, -- = -, +.+ = +, +/+ = +, -.- = +, -/- = +, +.- = -, +/- = -, -/+ = -

C: + = +, - = -,. = ., / = /, ~ = ~, = = =, =/= = =/=, =

D: + =/= -,. =/= /, ~ =/= -, = =/= =/=

E: =

1. a => a <=> a = a

2. ~a => ~a <=> ~a = ~a

3. a =/=> ~a <=> a =/= ~a

4. a ^ ɸ => a <=> a + 0 = a

5. a ^ ~ɸ => a <=> a - 0 = a

6. ~a ^ ɸ => ~a <=> ~a + 0 = ~a

7. ~a ^ ~ɸ => ~a <=> ~a - 0 = ~a

8. a v 1 => a <=> a.1 = a

9. a a <=> a/1 = a

10. ~a v 1 => ~a <=> ~a.1 = ~a

11. ~a ~a <=> ~a/1 = ~a

12. a v ɸ => ɸ <=> a.0 = 0

13. a < ɸ => ɸ <=> a/0 = 0

14. ~a v ɸ => ɸ <=> ~a.0 = 0

15. ~a < ɸ => ɸ <=> ~a/0 = 0

16. a ^ 1 => 1 ^ a <=> a + 1 = 1 + a

17. a ^ ~1 => Q ^ a <=> a - 1 = -1 + a

18. ~a ^ 1 => 1 ^ ~a <=> ~a + 1 = 1 + ~a

19. ~a ^ ~1 => Q ^ ~a <=> ~a - 1 = -1 + ~a

20. ɸ ^ a => a <=> 0 + a = a

21. ɸ ^ ~a => ~a <=> 0 - a = -a

22. ɸ ^ ~(~a) => !a <=> 0 - ~a = - ~a

23. a ^ a => a ^ a <=> a + a = a + a

24. a v a => a <=> a. a = a

25. a ^ ~a => e <=> a - a = 0

26. a 1 <=> a / a = 1

27. a v ~a => Q <=> a. ~a = 0

28. a ^ ~(~a) => a ^ !a <=> a - ~a = 1

29. a < ~a => Q <=> a / ~a = -1

30. a v b => b v a <=> a. b = b. a

31. a ^ b => b ^ a <=> a + b = b + a

32. (a ^ b) ^ c => a ^ (b ^ c) <=> (a + b) + c = a + (b + c)

33. (a v b) v c => a v (b v c) <=> (a . b). c = a. (b . c)

34. a ^ (b v c) => (a ^ b) v (a ^ c) <=> a + (b . c) = (a + b). (a + c)

35. a v (b ^ c) => (a v b) ^ (a v c) <=> a. (b + c) = (a . b) + (a . c)

36. ~(a ^ b) => ~a ^ ~b <=> ~(a + b) = ~a + ~b

37. ~(a v b) => ~a v ~b <=> ~(a . b) = ~a. ~b

38. a a < b <=> a / b = a / b

39. a ^ ~b => ~b ^ a <=> a - b = -b + a

40. (a ^ ~b) ^ ~c => a ^ (~b ^ ~c) <=> (a - b) - c = a (-b - c)

41.i.(a < b) a < (b v c) <=> (a / b) / c = a / (b . c)

41.ii. a < (b < c) => (a v c) < b <=> a / (b / c) = (a . c) / b

42. a ^ ~(b < c) => (a ^ ~b) < (a ^ ~c) <=> a - (b / c) = (a - b) / (a - c)

43. a < (b ^ ~c) => (a < b) ^ ~(a < c) <=> a / (b - c) = (a / b) - (a / c)

44. ~(a ^ ~b) => ~a ^ ~(~b) <=> ~(a - b) = ~a - ~b

45. ~(a < b) => ~a < ~b <=> ~(a / b) = ~a / ~b

46. ʘ => ʒ ^ e 47. ψa => a ^ ~a ^ !a 48. Эa => a v ~a v !a 49. ʒ => e 50. ɸ => ʒ ^ ~e

51. 1 => a < a 52. e => a ^ ~a 53. Q => ~ɸ ^ ~1 54. !a => ~(~a) 55. ʘ => ʒ ^ e < (Q ^ !e) v [(ɸ ^ 1) ^ (ψ ^ Э)]

zi': 0 + 0 = 0 <=> ɸ ^ ɸ => ɸ

zi": 0 - 0 = 0 <=> ɸ ^ ~ɸ => Q

zi"': 0 . 0 = 0 <=> ɸ v ɸ => ɸ

zi"": 0 / 0 = 0 <=> ɸ < ɸ => ∞

zii':0. 1 = 0 <=> ɸ v 1 => ɸ

zii": 1 . 0 = 0 <=> 1 v ɸ => ɸ

zii"': 0 / 1 = 0 <=> ɸ ɸ

zii"": 1 / 0 = 0 <=> 1 < ɸ => ɸ

ziii': 0. a = 0 <=> ɸ v a => ɸ

ziii": a . 0 = 0 <=> a v ɸ => ɸ

ziii"': 0 / a = 0 <=> ɸ ɸ

ziii"": a / 0 = 0 <=> a < ɸ => ɸ

ziv': 0. ~a = 0 <=> ɸ v ~a => ɸ

ziv": ~a . 0 = 0 <=> ~a v ɸ => ɸ

ziv"': 0 / ~a = 0 <=> ɸ < ~a => ɸ

ziv"": ~a / 0 = 0 <=> ~a < ɸ => ɸ

zv': 1 - 1 = 0 <=> 1 ^ ~1 => Q

zv": a - a = 0 <=> a ^ ~a => e

zv"': ~a - ~a = 0 <=> ~a ^ ~(~a) => !ɸ

zv"": a + ~a = 0 <=> a ^ ~a => e

G1. ЭX < ЭY G2. ЭX < Э~Y G3. ЭY < ЭX G4. ЭY < Э~X G5. Э~X < ЭY G6. Э~Y < ЭX G7. Э~X < Э~Y G8. Э~Y < Э~X G9. [~]X < ЭY G10. [~]Y < ЭX G11. [~]Y < Э~X G12. [~]~X < ЭY G13. [~]X < Э~Y G14. [~]~Y < ЭX G15. [~]~X < ~Y G16. [~]~Y < ~X

P1. (ЭX < ЭY) ^ ([~]Y < Э~X) => (ЭX < ψY) P2. (ЭX < Э~Y) ^ ([~]X < ЭY) => (ψX < Э~Y) P3. (ЭX < ЭY) ^ (ЭY < ЭX) => (ЭX < ЭY) P4. (Э~X < ЭY) ^ (ЭY < Э~X) => (Э~X < ЭY)

One.

1. (ψB < ~A) => (ψA < ~B) 2. (ЭA < ψC) ^ (ЭC < ЭB) =/=> [(ψB < ~A) <= (ЭC < ЭB)] 3. (ψB < ЭA) => (ЭA < ψB) 4. (ψA < ~B) => (ψB < ~A) 5. (ψB < ЭA) 6. (ЭB < ЭA) => (ЭA < ЭB) 7. (ψA < ~B) => (ψB < ~A) 8. (ЭB < ~A) => [(ЭA < ЭB) v (ψA < ~B)]

Two.

1. (ЭA < ψB) ^ (ЭB < ψC) => (ЭA < ψC) 2. (ψA < ~B) ^ (ЭB < ψC) => (ψA < ~C)

Three.

1. (ψB < ЭA) ^ (ЭC < ЭB) => (ЭC < ЭA) 2. (ψB < ~A) ^ (ЭC < ЭB) => (ЭC < ~A)

Four.

1. (ψA < ~B) ^ (ЭA < ψC) 2. (ψA < ~B) <=> (ψB < ~A) <= [(ψ < ~) <=> (~ < ψ)] 3. (ЭA < ψC) 4. (ψB < ~C) 5. (ЭA < ψB) ^ (ψA < ~C) => (ψB < ~C) 6. (ψA < ~C) => (ψC < ~A) 7. (ЭA < ψB) 8. (ψC < ~B) 9. (ψC < ~B) => (ψB < ~C)

Five.

1. (ψA < ~B) ^ (ЭA < ЭC) => (ЭC < ~B) 2. [(ψA < ~B) => (ψB < ~A)] <= [(ψ < ~) <=> (~ < ψ)] 3. (ЭA < ЭC) 4. (ЭC < ~B) 5. (ЭA < ψB) ^ (ψA < ~C) => (ψB < ~C) 6. (ЭB < ψC) ^ (ЭA < ψB) => (ЭA < ψC) 7. (ψA < ~C) 8. (ЭA < ψB) ^ (ЭC < ~A) => (ЭC < ~B)

Six.

1. (ЭA < ψB) ^ (ЭA < ЭC) 2. (ЭB < ψC) v (ψB < ~C) 3. (ψA < ~C) ^ (ЭA < ~B) 4. (ЭB < ψC) v (ψB < ~C)

Seven. 1. (ЭA < ψC) ^ (ЭB < ψC) => (ЭA < ЭB) 2. [(ЭB < ψC) <=> (ψC < ЭB)] <= [(Э < ψ) <=> (ψ < Э)] 3. (ЭA < ψC) ^ (ψC < ЭB) => (ЭA < ЭB)

Eight.

1. [(ЭA < ψC) ^ (ЭB < ψC)] ^ (ЭC < ψD) 2. [(ЭA < ψD) ^ (ЭB < ψD)] => (ЭA < ЭB) 3. (ЭB < ψC) ^ (ψA < ~C) => (ЭB < ~A)

Nine.

1. (ЭB < ψC) ^ (ЭA < ЭC) => (ЭA < ЭB) 2. [(ЭA < ЭC) <=> (ЭC < ЭA)] <= [(Э < Э) <=> (Э < Э)] 3. (ЭB < ψC) ^ (ЭC < ЭA) => (ЭB < ЭA)] 4. (ЭA < ЭB)]

Ten.

1. (ЭB < ЭC) ^ (ЭA < ψC) => (ЭA < ЭB) 2. (ЭB < ψC) ^ (ЭA < ~C) => (ЭA < ~B) 3. (ЭA < ψB) ^ (ЭB < ψC) => (ЭA < ψC) 4. (ЭA < ~C)

Eleven.

1. (ψA < ~C) ^ (ЭB < ЭC) => (ЭA < ~B)

Twelve.

1. [(ЭA < ψB) v (ЭA < ЭB)] ^ (ψB < ~C) 2. [(ψB < ЭA) v (ЭB < ЭA)] ^ (ψC < ~B) 3. (ЭA < ~C)

Thirteen.

1. (ЭA < ψC) ^ (ЭB < ψC) => (ЭA < ЭB) 2. (ψA < ~B) ^ (ЭB < ψC) => (ψA < ~C) 3. (ЭA < ψC)

Fourteen.

1. (ЭA < ψB) ^ (ЭB < ЭC) => (ЭA < ЭC) 2. (ψA < ~C) ^ (ЭA < ψB) => (ψB < ~C) 3. (ψA < ~B) ^ (ЭB < ЭC) => (ЭC < ~A) 4. (ЭA < ψC) ^ (ψA < ~B) => (ψB < ~C)

Fifteen. 1. (ЭA < ψB) ^ (ЭB < ЭC) 2. (ЭA < ЭC) 3. (ЭB < ЭC) ^ (ЭA < ψB)

Sixteen. 1. (ψB < ~A) ^ (ЭA < ψC) 2. [(ψB < ~A) => (ψA < ~B)] <= [(ψ < ~) => (~ < ψ)] 3. (ЭA < ψC) 4. (ψB < ~C) 5. (ψC < ЭA)

Seventeen. 1. (ψA < ~C) => (ψC < ~A) 2. (ЭA < ψB) 3. (ψC < ~B) 4. (ψB < ~C)

Eighteen. 1. (ψC < ~A) 2. (ψB < ~C) => (ψC < ~B) 3. (ЭB < ЭA) <= (ЭA < ψB) 4.(ψC < ~A)

Nineteen. 1. (ψB < ~A) ^ (ЭC < ЭA) 2. (ψB < ~A) => (ψA < ~B) 3. (ЭC < ЭA) 4. (ЭB < ~C)

Twenty. 1. (ЭA < ψB) ^(ЭC < ~A) => (ЭC < ~B)

Twenty One. 1. (ЭA < ψC) ^ (ЭB < ψC) 2. [(ЭB < ψC) => (ЭC < ЭB)] <= [(Э < ψ) => (Э < Э)] 3. (ЭA < ψC) ^ (ЭC < ЭB) => (ЭA < ЭB) 4. (ЭC < ЭB)

Twenty Two. 1. (ЭC < ЭA) => (ЭA < ЭC) 2. (ЭB < ψC) => (ЭB < ЭA)

Twenty Three. 1. (ψA < ~C) ^ (ЭB < ЭC) 2. (ЭB < ЭC) ^ (ψA < ~C) => (ЭA < ~B) 3. (ЭB < ЭC)

Twenty Four. 1. (ЭB < ЭC) ^ (ψA < ~C) 2. (ЭB < ЭC) => (ЭC < ЭB) 3. (ψA < ~C) ^ (ЭB < ЭC) => (ЭA < ~B)

Twenty Five. 1. (ЭB < ψC) ^ (ЭA < ЭC) => (ЭB < ЭA) 2. (ψA < ~C) ^ (ЭB < ЭC) => (ЭB < ~A)

Twenty Six. 1. [(ЭA < ψB) v (ЭA < ЭB)] ^ (ЭB < ψC) 2. (ЭA < ψC) v (ЭA < ЭC) 3. [(ψA < ~B) v (ЭA < ~B)] ^ (ЭB < ψC) 4. (ψA < ~C) v (ЭA < ~C) 5. {[(ЭA < ψB) v (ЭA < ЭB)] ^ (ЭB < ЭC)} => [(ЭA < ψC) v (ЭA < ЭC)]

Twenty Seven. 1. {[(ψA < ~B) v (ЭA < ~B)] ^ (ЭB < ЭC)} => [(ψA < ~C) v (ЭA < ~C)]

Twenty Eight. 1. [(ЭA < ψB) v (ЭA < ЭB)] ^ (ЭB < ψC) 2. {(ЭB < ψC) ^ [(ЭA < ψB) v (ЭA < ЭB)]} => [(ЭA < ψC) v (ЭA < ЭC)]

Twenty Nine. 1. {[(ψA < ~B) v (ЭA < ~B)] ^ (ЭB < ψC )} => [(ψA < ~C) v (ЭA < ~C)]

Thirty. 1. A < B 2. [(A <= B) v (A => B v ~B)] ^ (~A => ~B) 3. (A v ~A) ^ ~B 4. (A v ~A) => (A v ~A) 5. ~B => ~B 6. (A v ~A) ^ ~B 7. [(A ^ ~B) v (~A ^ ~B)] => [(A < A) ^ (A => A)] 8. (A => A) <=> (A < A)

Thirty One. 1. (A v ~A) ^ (A < B) => [(A => B) v (~A => ~B)] 2. A <= B 3. {[(A => B v ~B) v (~A => ~B)] ^ (A v ~A)} => (B v ~B) 4. (~B v ~B) => [(~B v ~B) ^ (B v ~B)]

Thirty Two. 1. (~B v ~B) ^ ~(B v B) ^ ~(ψB v ЭB) 2. (ЭB < ψC) 3. (ψA < ~C) ^ (ЭB < ψC) => [(ЭA < ~B) v (ψA < ~B)] 4. (ЭA < ψB) v (ЭA < ЭB) 5. (ЭA < ψC) v (ЭA < ЭC) 6. (ψA < ~C) <=/=> [(ЭA < ψC) v (ЭA < ЭC)]

Thirty Three. 1. B < C 2. {(ЭB < ψC) ^ [(ЭA < ψB) v (ЭA < ЭB)]} => [(ЭA < ψC) v (ЭA < ЭC)] 3. (ψA < ~C) v (ЭA < ~C)

Thirty Four. 1. (ψA < ~B) ^ [(ЭB < ψC) v (ЭB < ЭC)] 2. (ЭA < ~C) v (ψA < ~C) 3. (ψA < ~C) ^ [(ЭB < ψC) v (ЭB < ЭC)] 4. (ЭA < ЭB) 5. (ψA < ~B) <=/=> (ЭA < ЭB) 6. (ψA < ~C)

Thirty Five. 1. (ЭA < ψB) ^ [(ψB < ~C) v (ЭB < ~C)] 2. (ЭA < ~C) v (ЭA < ~C) 3. (ЭB < ψC) v (ЭB < ЭC) 4. {(ЭA < ψB) ^ [(ЭB < ψC) v (ЭB < ЭC)]} => [(ЭA < ψC) v (ЭA < ЭC)]

Thirty Six. 1. (ψA < ~B) ^ [(ЭB < ~C) v (ψB < ~C)] 2. [(ЭA < ψC) v (ЭA < ЭC)] v [(ЭA < ~C) v (ψA < ~C)] 3. {(ЭA < ψB) ^ [(ЭB < ~C) v (ψB < ~C)]} => [(ЭA < ~C) v (ψA < ~C)]

Thirty Seven. 1. (ψA < ~B) ^ [(ЭB < ~C) v (ψB < ~C)] 2. [(ЭA < ψC) v (ЭA < ЭC)] v [(ЭA < ~C) v (ψA < ~C)] 3. {[(ЭB < ψC) v (ЭB < ЭC)] ^ (ψA < ~B)} => [(ЭA < ~C) v (ψA < ~C)]

Thirty Eight. 1. (ЭA < ψB) ^ [(ЭB < ψC) v (ЭB < ЭC)] 2. [(ЭA < ψC) v (ЭA < ЭC)]

Thirty Nine. 1. [(ЭA < ψB) v (ЭA < ЭB)] ^ (ЭB < ψC) 2. [(ЭA < ЭC) v (ЭA < ψC)] =/=> (ЭA < ψC)]

Forty. 1. (ψB < ~A) ^ [(ЭB < ЭC) v (ЭB < ψC)] 2. (ψA < ~C) 3. [(ЭA < ЭC) v (ЭA < ψC)] 4. (ψB < ~A) 5. (ψB < ~A) => (ψA < ~B) 6. [(ЭA < ЭC) v (ЭA < ψC)] 7. [(ЭB < ~C) v (ψB < ~C)] 8. [(ЭB < ЭC) v (ЭB < ψC)]

Forty One. 1. (ψB < ~A) ^ [(ЭB < ЭC) v (ЭB < ψC)] 2. (ЭA < ~C) 3. (ЭA < ψC) ^ [(ψB < ~A) => (ψA < ~B)] 4. (ЭA < ψC) => (ψC < ~B) 5. [(ЭB < ЭC) v (ЭB < ψC)]

Forty Two. 1. (ψA < ~B) ^ (ЭA < ψC) 2. (ψA < ~B) => (ψB < ~A) 3. (ЭA < ψC) 4. (ψB < ~A) ^ (ЭA < ψC) => (ψB < ~C)

Forty Three. 1. (ψB < ~A) ^ [(ЭA < ψC) v (ЭA < ЭC)] 2. (ψB < ~A) => (ψA < ~B) 3. [(ЭA < ψC) v (ЭA < ЭC)] 4. {(ψA < ~B) ^ [(ЭA < ψC) v (ЭA < ЭC)]} => [(ψC < ~B) v (ЭC < ~B)] 5. (ψC < ~B) 6. (ЭC < ЭB) 7. (ψA < ~B) ^ (ЭC < ЭB) => (ЭA < ~C) 8. [(ЭA < ψC) v (ЭA < ЭC)]

Forty Four. 1. (ψB < ~A) ^ [(ψC < ~A) v (ЭC < ~A) v (ЭC < ЭA)] 2. (ψB < ~A) => (ψA < ~B) 3. (ЭA < ψC) 4. (ψA < ~B) ^ (ЭA < ψC) => (ψB < ~C)

Forty Five. 1. [(ЭA < ψC) v (ЭA < ЭC)] ^ [(ЭB < ψC) v (ЭB < ЭC)] 2. [(ЭB < ψC) v (ЭB < ЭC)] => [ψC < ЭB) v (ЭC < ЭB)] 3. [(ЭA < ψC) v (ЭA < ЭC)] ^ [ψC < ЭB) v (ЭC < ЭB)] 4. (ЭA < ЭB) v (ψA < ~B)

Forty Six. 1. [(ψC < ~A) v (ЭC < ЭA)] ^ [(ЭB < ψC) v (ЭB < ЭC)] 2. (ЭB < ~A) v (ЭB < ЭA)

Forty Seven. 1. [(ψC < ~A) v (ЭC < ~A)] ^ [(ψC < ~B) v (ЭC < ~B)] 2. [(ψB < ~A) v (ЭB < ~A)] v [(ЭB < ψA) v (ЭB < ЭA)] 3. {[(ЭA < ψC) v (ЭA < ЭC)] ^ [(ЭB < ψC) v (ЭB < ЭC)]} => [(ЭB < ψA) v (ЭB < ЭA)]

Forty Eight. 1. [(ЭA < ψC) v (ЭA < ЭC)] ^ (ЭB < ЭC) 2. (ЭB < ЭC) => (ЭC < ЭB)] 3. {[(ЭA < ψC) v (ЭA < ЭC)] ^ (ЭC < ЭB)} => [(ЭA < ЭB) v (ЭA < ~B)]

Forty Nine. 1. (ЭA < ψC) ^ [(ЭB < ψC) v (ψB < ~C)] 2. [(ЭB < ψC) v (ψB < ~C)] => [(ψC < ЭB) v (ψC < ~B)] 3. {(ЭA < ψC) ^ [(ψC < ЭB) v (ψC < ~B)]} => [(ЭA < ЭB) v (ЭA < ~B)]

Fifty. 1. (ЭB < ψC) ^ [(ЭA < ЭC) v (ЭA < ~C)] 2. [(ЭA < ЭB) v (ЭA < ~B)] 3. (ЭA < ψB) ^ (ЭB < ψC) 4. (ЭA < ψC) 5. [(ЭA < ЭC) v (ЭA < ~C)]

Fifty One. 1. (ЭA < ψC) ^ [(ЭB < ψC) v (ЭB < ЭC)] 2. (ЭA < ψC) ^ [(ЭC < ЭB) v (ψC < ЭB)] 3. [(ЭB < ψA) v (ЭB < ЭA)]

Fifty Two. 1. A=>B, C=>A, D=/=>A. 2. E=>F, G=>E, H=/=>E. 3. C <=> F => ЭA < ψE. 4. (ЭF < ψE) ^ (ЭA < ψC) => (ЭA < ψE) 5. [(C <=> G) => (ЭA < ЭE)] <= [(C=>A) ^ (G=>E)] 6. (F <=> D) => (ψA < ~E) 7.{[(ψA < ~E) => (ψE < ~A)] ^ (F <=> D)} => [(ψA < ~F) ^ (ЭF < ψE)].

Fifty Three. 1. (B <=> H) => (ψA < ~E). 2. (ЭB < ψA) ^ (ψB < ~E). 3. (B <=> H) ^ (ψH < ~E).

Fifty Four. 1. (D <=> G) => [(ψA v ЭA) < ~E.] 2. (ψA < ~G) <= (ψA < ~D). 3. ψG < ЭE. 4. (ψA v ЭA) < ~E.

Fifty Five. 1. (B <=> G). 2. (ЭE < ψA) <= {[(ψB < ЭA) ^ (ψE < ЭB)] ^ (B <=> G)}. 3. (ЭA < ψE) v (ЭA < ЭE). 4. (ЭA < ЭE) <= (ψ => Э) 5. (ЭC <=> ЭF) => (ЭA < ψE)

Fifty Six. 1. (C <=> G) => (ЭA <=> ЭE) 2. (ЭD <=> ЭF) => (ψA < ~E) 3. [(ψA < ~F) <= {(ψF < ~A)] ^ (ЭF < ψE)} 4. (ψD < ~A) ^ (ЭD < ψE) 5. (ЭD <=> ЭG) => (ψA < ~E) 6. (ψA < ~G) ^ (ЭE < ψG)

S1. (ЭC < ψB) ^ (ЭB < ψA) => (ЭC < ψA) S2. (ψC < ~B) ^ (ЭB < ψA) => (ψC < ~A) S3. (ЭC < ψB) ^ (ЭB < ЭA) => (ЭC < ЭA) S4. (ψC < ~B) ^ (ЭB < ЭA) => (~C < ЭA) S5. (ψB < ~C) ^ (ЭB < ψA) => (ψC < ~A) S6. (ЭB < ψC) ^ (ψB < ~A) => (ψC < ~A) S7. (ψB < ~C) ^ (ЭB < ЭA) => (~C < ЭA) S8. (ЭB < ψC) ^ (~B < ЭA) => (~C < ЭA) S9. (ЭC < ψB) ^ (ЭA < ψB) => (ЭC < ЭA) S10. (ψC < ~B) ^ (ЭA < ψB) => (~C < ЭA) S11. (ЭC < ЭB) ^ (ЭA < ψB) => (ЭC < ЭA) S12. (ЭC < ψB) ^ (ЭA < ЭB) => (ЭC < ЭA) S13. (~C < ЭB) ^ (ЭA < ψB) => (~C < ЭA) S14. (ψC < ~B) ^ (ЭA < ЭB) => (~C < ЭA) S15.(ЭB < ψC) ^ (ЭA < ψB) => (ψC < ЭA) S16.(ЭB < ψC) ^ (ψA < ~B) => (~C < ψA) S17.(ЭB < ЭC) ^ (ЭA < ψB) => (ЭC < ЭA) S18.(ψB < ~C) ^ (ЭA < ψB) => (~C < ЭA) S19.(ψB < ~C) ^ (ЭA < ЭB) => (~C < ЭA)

1. (ЭC < ψA) 1.1 (ЭC < ψB) ^ (ЭB < ψA)

2. (ψC < ~A) 2.1 (ψC < ~B) ^ (ЭB < ψA) 2.2 (ψB < ~C) ^ (ЭB < ψA) 2.3 (ЭB < ψC) ^ (ψB < ~A)

3. (ЭC < ЭA) 3.1 (ЭC < ψB) ^ (ЭB < ЭA) 3.2 (ЭC < ψB) ^ (ЭA < ψB) 3.3 (ЭC < ψB) ^ (ЭA < ЭB) 3.4 (ЭC < ЭB) ^ (ЭA < ψB) 3.5 (ЭB < ψC) ^ (ЭA < ψB) 3.6 (ЭB < ЭC) ^ (ЭA < ψB)

4.(~C < ЭA) 4.1 (ψC < ~B) ^ (ЭB < ЭA) 4.2 (ψB < ~C) ^ (ЭB < ЭA) 4.3 (ЭB < ψC) ^ (~B < ЭA) 4.4 (ψC < ~B) ^ (ЭA < ψB) 4.5 (~C < ЭB) ^ (ЭA < ψB) 4.6 (ψC < ~B) ^ (ЭA < ЭB) 4.7 (ЭB < ψC) ^ (ψA < ~B) 4.8 (ψB < ~C) ^ (ЭA < ψB) 4.9 (ψB < ~C) ^ (ЭA < ЭB)

Corrections to the original article will be notified here.

Adjustive corrections have since been made to: 41, giving 41.i, 41.ii. Adjustive corrections have also been made to S15 and S16.

See also: https://en.wikiversity.org/w/index.php?title=User:Shadowjack/Deductive_logic&oldid=1129397

https://en.wikiversity.org/w/index.php?title=User:Glimmerguard/Quantum_Indefinite&oldid=1127754

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