Re: [請益] 數理邏輯 The Predicate Calculus. Val …

[yauhh (喲)]

※ 引述《priest0204 (香香)》之銘言：
: Let x and y be variables, A(x),B(x), and A(x,y) be any formulas,
: and A be any formula not containing any free occurrences of x.
: Then
: 1.╞(exist x)(A(x)orB(x))←→(exist x)A(x)or(exist x)B(x)
...
: Discuss the validity of formulas 1

(exist x)(Ax or Bx)
-> ~ ~(exist x)(Ax or Bx)
-> ~ (for all x) ~(Ax or Bx)
-> ~ (for all x) (~Ax and ~Bx)
-> ~ ((for all x) ~Ax and (for all x) ~Bx)
-> ~ (for all x) ~Ax or ~(for all x) ~Bx
-> ~ ~(exist x) Ax or ~ ~(exist x) Bx
-> (exist x) Ax or (exist x) Bx

(exist x) Ax or (exist x) Bx
-> ~ ~(exist x) Ax or ~ ~(exist x) Bx
-> ~ (for all x) ~Ax or ~ (for all x) ~Bx
-> ~ ((for all x) ~Ax and (for all x) ~Bx)
-> ~ (for all x) (~Ax and ~Bx)
-> ~ (for all x) ~(Ax or Bx)
-> ~ ~(exist x)(Ax or Bx)
-> (exist x)(Ax or Bx)


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