SOLUTION: Need help writing out this proof using induction and elimination rules. (E V B) --> ~D S V D E goal: S also: (P ^ ~Q) --> ~(P <-> Q) Prove goal without premises

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Question 1078186: Need help writing out this proof using induction and elimination rules.
(E V B) --> ~D
S V D
E
goal: S
also:
(P ^ ~Q) --> ~(P <-> Q)
Prove goal without premises
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
1. (E V B) --> ~D
2.  S V D
3.  E          /S

4. E V B       3, addition
5. ~D          1,4, modus ponens
6. D V S       2, commutation
7. S           6,5, disjunctive syllogism

-----------------------------

You didn't specify a method, so truth table
is as good as any (without premises), since
there are only two variables.

(P ^ ~Q) --> ~(P <-> Q)
 T F FT  T   F T  T  T
 T T TF  T   T T  F  F
 F F FT  T   T F  F  T
 F F TF  T   F F  T  F 

It is valid because there are only T's under the -->

Edwin