You can put this solution on YOUR website! I'm going to use a conditional proof. So that means we assume E is true (line 3). If we can show it leads to A (line 12), then E > A is true.
Number
Statement
Lines Used
Reason
1
~(A & B) = ~C
2
(D v E) > C
.:
E > A
3
E
ACP
4
E v D
3
Add
5
D v E
4
Comm
6
C
2,5
MP
7
~~C
6
DN
8
[~(A & B) > ~C] & [~C > ~(A & B)]
1
ME
9
~(A & B) > ~C
8
Simp
10
~~(A & B)
9,7
MT
11
A & B
10
DN
12
A
11
Simp
13
E > A
3-12
CP
Abbreviations/Acronyms Used:
ACP = Assumption for Conditional Proof
Add = Addition
Comm = Commutation
CP = Conditional Proof
DN = Double Negation
ME = Material Equivalence
MP = Modus Ponens
MT = Modus Tollens
Simp = Simplification
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