SYMBOLIC LOGIC Cant use constructive proofs 1 C B A D

SYMBOLIC LOGIC

Can\'t use constructive proofs:

1. (~ C -> ~ B) -> (~ A -> D)      Premise

    2. H -> C                                     Premise

    3. ~ H -> ~ B                               Premise

    4. ~ D                                       Premise conclusion: ~ ~ A

Solution

1. (~ C -> ~ B) -> (~ A -> D)     

2. H -> C                                  

3. ~ H -> ~ B                            

4. ~ D     

H implies C

and from # 1 not C impiies not B

so C implies B

so as H implies C

then Not H will imply not B

and as not C impies Not B is true

then not A implies not D will also be true

hence not D will imply A

or NOt D will imply not not A

hence conclusion is true

not D implies not not A