In Symbolic Logic, how do you go from the premise ¬(A ∨ B) to the goal ¬A ∧ ¬B?
I know they essentially mean the same thing, but what would the proof look like?
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I know they essentially mean the same thing, but what would the proof look like?
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de morgan's rule ~(AvB)=~A*~B and ~(A*B)=~Av~B one of the laws of equivalence
Easily - De Morgans Law. But let me recreate that proof and get back to you.
- (A v B) (Assumption)
A (Provisional Assumption)
A v B (Addition)
- (A v B) (Reiteration)
-A (Indirect Proof)
B (PA)
A v B (Add.)
-(AvB) (Reit.)
-B (IP)
-A & -B (Conjunction)
Let me explain how I got there. 1 sec.