ƒy / (x)ƒx UG where the VARIABLE y is free in ƒy in EXACTLY those places that x is bound in ƒx by the quantifier (x)
CORRECT
|
1. 2. |
(x)Axy (y)(x)Axy |
1,UG |
INcorrect
|
1. 2. |
(x)Axy (x)Axx |
1,UG |
X since the (x) controls the place where y was free and others as well. |
CORRECT
|
... 7. 8. |
Axa (z)Aza |
7,UG |
INcorrect
|
... 7. 8. |
Axa (y)Axy |
7,UG |
X since a is NOT an x y z |
CORRECT
|
1. 2. 3. 4. |
(∃y)[Ax • By] Ax • Ba Ax (x)Ax |
1,EI 2,simp 3,UG |
INcorrect
|
1. 2. 3. |
(∃y)Axy Axa (x)Axa |
1,EI 1,EI |
X since line #3 contains a and x is free in line #2 where a was introduced. |
CORRECT
| 3. | Ax | ||
| |4. Bx |5. Bx • Ax |
ACP 4,3,conj |
||
| 6. 7. |
Bx ⊃ (Bx•Ax) (x)[Bx ⊃ (Bx•Ax)] |
CP 4-5 6,UG |
INcorrect
| 3. | Ax | |||
| |4. |5. |
Bx (x)Ax |
ACP 3 UG |
X since this UG is within the scope of an ACP (or AIP) and x is free in the ACP (AIP). |