→ priest0204:感謝大大的幫忙 01/19 21:07
※ 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)
反證法
2.~ (exist x)A(x)or(exist x)B(x)求矛盾
3.~(Ex)Ax and ~(Ex)Bx DeM
4.Ax or Bx 1,EI
5.~Ax 3,Simp,EI
6.Bx 4,5 DS
7.~Bx 3,Simp,EI
8.Bx and ~Bx 6,7 Conj
9. (exist x)A(x)or(exist x)B(x) 2-8 ,IP
: 2.╞(for all x)A(x)or(for all x)B(x)→(for all x)(A(x)orB(x))
反證法
2.~ (x) A(x) or B(x) 求矛盾
3.(Ex)~(Ax or Bx) 2,QN
4.~(Ax or Bx) 3,EI
5.Ax or Bx 1,UI
6.~(5) and (5) 4,5 Conj
7.(for all x)(A(x)orB(x)) 2-6,IP
: 3.╞(exist x)(AorB(x))←→Aor(exist x)B(x)
反證法
2. ~(A or (Ex)Bx) 求矛盾
3. ~A and ~(Ex)Bx 2,DeM
4. A or Bx 1,EI
5.~A 3,Simp
6.Bx 4,5 DS
7.(Ex)Bx 6,EG
8.~(Ex)Bx 2,Simp
9. (7) and~(7) 7,8 Conj
10. Aor(exist x)B(x) 2-9 IP
: Discuss the validity of formulas 1,2 and 3
先回前三題
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