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I am proving the follow argument

[(A ↔ B ) → C] ⊢ [ - ( A ^ B) V C ]

Using the following set of rules

I, ^E, vI, vE, →I, →E, ↔I, ↔E, --E, -I

Here are my steps but I got to the point where I couldn't discharge an assumption. I need to know know if my steps are correct, if not, I hope someone can correct me here. I'm kind of confident that my steps are right except for not discharging -C assumption on line 2.

Here are my steps

1) [(A ↔ B ) → C]       A
2) -C                   A
3) A ^ B                A    for (-I)
4) A                    3    ^E
5) B                    3    ^E
6) A → B                4,5  →I
7) B → A                4,5  →I
8) (A → B) ^ (B → A)    6,7  ^I
9) A ↔ B                8    ↔I
10)C                    1,9  →E 
11)C^-C                 2,10 ^I
12)-(A^B)               3,11 -I //discharged (A^B , line 3 (A^B)
13)-(A^B) V C           12    vI

Are my steps valid ? How do I discharge line 2? Please show me, thanks!

I am proving the follow argument

[(A ↔ B ) → C] ⊢ [ - ( A ^ B) V C ]

Using the following set of rules

I, ^E, vI, vE, →I, →E, ↔I, ↔E, --E, -I

Here are my steps but I got to the point where I couldn't discharge an assumption. I need to know know if my steps are correct, if not, I hope someone can correct me here. I'm kind of confident that my steps are right except for not discharging -C assumption on line 2.

Here are my steps

1) [(A ↔ B ) → C]       A
2) -C                   A
3) A ^ B                A    for (-I)
4) A                    3    ^E
5) B                    3    ^E
6) A → B                4,5  →I
7) B → A                4,5  →I
8) (A → B) ^ (B → A)    6,7  ^I
9) A ↔ B                8    ↔I
10)C                    1,9  →E 
11)C^-C                 2,10 ^I
12)-(A^B)               3,11 -I //discharged (A^B , line 3)
13)-(A^B) V C           12    vI

Are my steps valid ? How do I discharge line 2? Please show me, thanks!

I am proving the follow argument

[(A ↔ B ) → C] ⊢ [ - ( A ^ B) V C ]

Using the following set of rules

I, ^E, vI, vE, →I, →E, ↔I, ↔E, --E, -I

Here are my steps but I got to the point where I couldn't discharge an assumption. I need to know know if my steps are correct, if not, I hope someone can correct me here. I'm kind of confident that my steps are right except for not discharging -C assumption on line 2.

Here are my steps

1) [(A ↔ B ) → C]       A
2) -C                   A
3) A ^ B                A    for (-I)
4) A                    3    ^E
5) B                    3    ^E
6) A → B                4,5  →I
7) B → A                4,5  →I
8) (A → B) ^ (B → A)    6,7  ^I
9) A ↔ B                8    ↔I
10)C                    1,9  →E 
11)C^-C                 2,10 ^I
12)-(A^B)               3,11 -I //discharged line 3 (A^B)
13)-(A^B) V C           12    vI

Are my steps valid ? How do I discharge line 2? Please show me, thanks!

Source Link
cookie monster
cookie monster
  • 65
  • 5

How to discharge an assumption?

I am proving the follow argument

[(A ↔ B ) → C] ⊢ [ - ( A ^ B) V C ]

Using the following set of rules

I, ^E, vI, vE, →I, →E, ↔I, ↔E, --E, -I

Here are my steps but I got to the point where I couldn't discharge an assumption. I need to know know if my steps are correct, if not, I hope someone can correct me here. I'm kind of confident that my steps are right except for not discharging -C assumption on line 2.

Here are my steps

1) [(A ↔ B ) → C]       A
2) -C                   A
3) A ^ B                A    for (-I)
4) A                    3    ^E
5) B                    3    ^E
6) A → B                4,5  →I
7) B → A                4,5  →I
8) (A → B) ^ (B → A)    6,7  ^I
9) A ↔ B                8    ↔I
10)C                    1,9  →E 
11)C^-C                 2,10 ^I
12)-(A^B)               3,11 -I //discharged (A^B , line 3)
13)-(A^B) V C           12    vI

Are my steps valid ? How do I discharge line 2? Please show me, thanks!