Step by Step solution about How to resolve the algorithm Ternary logic step by step in the Julia programming language

This code implements the operations of a ternary logic system in Julia programming language. It defines an @enum called Trit with three values: False, Maybe, and True.

It then defines four functions: !, ∧, ∨, ⊃, and ≡, which implement the logical NOT, AND, OR, IMPLICATION, and EQUIVALENCE operations, respectively.

Next, it prints out a table for each operation, showing the result of the operation for all possible combinations of input values.

NOT

Not (!):
! False is True
! Maybe is Maybe
! True  is False

AND

And (∧):
False ∧ False is False
False ∧ Maybe is False
False ∧ True  is False
Maybe ∧ False is False
Maybe ∧ Maybe is Maybe
Maybe ∧ True  is Maybe
True  ∧ False is False
True  ∧ Maybe is Maybe
True  ∧ True  is True

OR

Or (∨):
False ∨ False is False
False ∨ Maybe is Maybe
False ∨ True  is True
Maybe ∨ False is Maybe
Maybe ∨ Maybe is Maybe
Maybe ∨ True  is True
True  ∨ False is True
True  ∨ Maybe is True
True  ∨ True  is True

IMPLICATION

If Then (⊃):
False ⊃ False is True
False ⊃ Maybe is Maybe
False ⊃ True  is True
Maybe ⊃ False is False
Maybe ⊃ Maybe is Maybe
Maybe ⊃ True  is Maybe
True  ⊃ False is False
True  ⊃ Maybe is False
True  ⊃ True  is True

EQUIVALENCE

Equivalent (≡):
False ≡ False is True
False ≡ Maybe is False
False ≡ True  is False
Maybe ≡ False is False
Maybe ≡ Maybe is Maybe
Maybe ≡ True  is False
True  ≡ False is False
True  ≡ Maybe is False
True  ≡ True  is True

@enum Trit False Maybe True
const trits = (False, Maybe, True)

Base.:!(a::Trit) = a == False ? True : a == Maybe ? Maybe : False
∧(a::Trit, b::Trit) = a == b == True ? True : (a, b) ∋ False ? False : Maybe
∨(a::Trit, b::Trit) = a == b == False ? False : (a, b) ∋ True ? True : Maybe
⊃(a::Trit, b::Trit) = a == False || b == True ? True : (a, b) ∋ Maybe ? Maybe : False
≡(a::Trit, b::Trit) = (a, b) ∋ Maybe ? Maybe : a == b ? True : False

println("Not (!):")
println(join(@sprintf("%10s%s is %5s", "!", t, !t) for t in trits))
println("And (∧):")
for a in trits
    println(join(@sprintf("%10s ∧ %5s is %5s", a, b, a ∧ b) for b in trits))
end
println("Or (∨):")
for a in trits
    println(join(@sprintf("%10s ∨ %5s is %5s", a, b, a ∨ b) for b in trits))
end
println("If Then (⊃):")
for a in trits
    println(join(@sprintf("%10s ⊃ %5s is %5s", a, b, a ⊃ b) for b in trits))
end
println("Equivalent (≡):")
for a in trits
    println(join(@sprintf("%10s ≡ %5s is %5s", a, b, a ≡ b) for b in trits))
end