SOLUTION: I know that these two conjuncts are equivelant, but I do not know how to solve/show this! prove ~(pvq) |- ~p &~q

Algebra ->  Proofs -> SOLUTION: I know that these two conjuncts are equivelant, but I do not know how to solve/show this! prove ~(pvq) |- ~p &~q      Log On


   

Question 188797: I know that these two conjuncts are equivelant, but I do not know how to solve/show this!
prove ~(pvq) |- ~p &~q
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You can use a truth table to prove this statement:

pq~p~qp v q~(p v q) ~p & ~q
TTFFTFF
TFFTTFF
FTTFTFF
FFTTFTT



Notice how the columns in red have the same truth values. So this shows that the last columns are logically equivalent.