Natural deduction question

[TaniaRaza]

I am proving it valid by natural deduction.. Can someone please tell me if there is any mistake



1 B → (C ⇔ D) Premise

2 B Premise

3 ~C Premise

4 C ⇔ D =>E 1,2

5 D → C =>E 4

6 D Assumption

7 D → C

8 C =>E 5,7

9 ~C

10 ~D

 

[blamocur]

I am proving it valid by natural deduction.. Can someone please tell me if there is any mistake



1 B → (C ⇔ D) Premise

2 B Premise

3 ~C Premise

4 C ⇔ D =>E 1,2

5 D → C =>E 4

6 D Assumption

7 D → C

8 C =>E 5,7

9 ~C

10 ~D

What are you proving?

 

[TaniaRaza]

What are you proving?

Validity of argument by natural deduction derivation

 

[blamocur]

Validity of argument by natural deduction derivation

I am still confused: validity of which argument?

 

[pka]

I am still confused: validity of which argument?

@blamocur, do you know what Natural Deduction is all about? SEE THIS LINK
As you will see it was put by the Polish logical group in the 1930's.
I am decidedly not a fan myself.

 

[blamocur]

@blamocur, do you know what Natural Deduction is all about? SEE THIS LINK
As you will see it was put by the Polish logical group in the 1930's.
I am decidedly not a fan myself.

No, I had no clue -- thanks for the link. Definitely not my cup of tea

 

[chrislav]

I am proving it valid by natural deduction.. Can someone please tell me if there is any mistake



1 B → (C ⇔ D) Premise

2 B Premise

3 ~C Premise

4 C ⇔ D =>E 1,2

5 D → C =>E 4

6 D Assumption

7 D → C

8 C =>E 5,7

9 ~C

10 ~D

the justification of line 4 is wrong the correct is: 1,2 modus ponens
line 8 is wrong again we have again 5,6and M.P
line 7 is not needed at all
Your asumption at line 6 should read :assumption for contradiction that is if you want to prove ~D
Line 9 should read C &~C BY LINES 3,8 AND using addition introduction
Here now we have contradiction ,hence the conclusion is ~D
of course there is a shorter way to prove ~D