How do I negate ~p <-> q (biconditional statement)?

Answer 1

~p <--> q = ~p -->q and q-->~p

= (p v q) and (~q v ~p)

Negating with DeMorgan's Rule:

~[ (p v q) and (~q v ~p)] =

~( p v q) or ~(~q v ~p) =

(~p and ~q) or (q and p) <---- please label this equation ALPHA

p q ~p ~p -->q q --> ~p ~p<-->q ~(~p <--> q) | ~p and ~q q and p ALPHA

T T F T F F T F T T

T F F T T T F F F F

F T T T T T F F F F

F F T F T F T T T T

notice that equation ALPHA has the same truth values, row by row, as the negation of the binomial.