SOLUTION: Truth Table: ~(P=>Q)<=>(P^~Q) I believe I am on the right path with the following: P Q P=>Q ~(P=>Q) ~Q P^~Q t t t t f t f t t

Algebra ->  Conjunction -> SOLUTION: Truth Table: ~(P=>Q)<=>(P^~Q) I believe I am on the right path with the following: P Q P=>Q ~(P=>Q) ~Q P^~Q t t t t f t f t t       Log On


   



Question 385135: Truth Table: ~(P=>Q)<=>(P^~Q)
I believe I am on the right path with the following:
P Q P=>Q ~(P=>Q) ~Q P^~Q
t t t t f t
f t t f f f
t f f t t t
f f t f t f
Making this table a neither a tautology or a contrdiction. Would this be correct? Six columns with 4 t or f under each column. They would not line up for me so I hope this is understandable.
Melody

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The truth table for ~(P=>Q)<=>(P^~Q) is

PQP => Q~(P => Q)~QP ^ ~Q~(P => Q) <=> (P ^ ~Q)
TTTFFFT
TFFTTTT
FTTFFFT
FFTFTFT



which means that we have a tautology (because the last column has nothing but T in it).


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim