a=superman is able to prevent evil

b= superman is impotent

c=superman is willing to prevent evil

d=superman is malevolent

e= superman exsists

f= superman prevents evil

 

argument form=

(a∧c)→f

¬a→b

¬c→d

¬f

e→¬b∧¬d

___________________

:.¬e

 

Argument =

(we have to prove ¬e)

 

  1.  (a∧c)→f    =”p”→f  =add  !f  =  apply modus tollens   (!f∧(p→f))→!p = !p = !(a∧c)
  2.  ¬ (a∧c)  =  !a V !c

¬a→b

¬c→d

 

e→¬(b∧d)

 

*i am lost after this

i know this is supposed to look like this

and pg 73 of the book has it but i dont really understand how the substituting works

 

this website explains more about building arguments:

http://sites.millersville.edu/bikenaga/math-proof/rules-of-inference/rules-of-inference.html