Can we treat p↔q and ¬(p⊕q) the same thing? They actually share the same truth value, but it just seems a little strange.

Question

anonymous · Answer

Since there are only two variables, p and q,  you could just write out a truth table and find out if it is a tautology.

directrix · Answer

@RolyPoly What is this symbol that you posted? See attachment?

anonymous · Answer

`$\oplus$` $\oplus$

anonymous · Answer

¬ ---> not
⊕ ---> exclusive or

directrix · Answer

Is that the same as   ~ ( p v q)  which I would read as "not p or q".

anonymous · Answer

p  q   p↔q  (p⊕q)  ¬(p⊕q) 
T  T      T        F          T
T  F      F       T           F
F  T      F       T           F
F  F      T        F          T

So, they are tautology, as I've mentioned. Though, isn't it a bit strange?

anonymous · Answer

@Directrix Exactly one is true.

anonymous · Answer

@Directrix Not really.
p  q   pvq  (p⊕q)  
T  T      T       F   
T  F      T       T     
F  T      T       T     
F  F       F       F

directrix · Answer

Well, I've learned something new.

The statement A ⊕ B is true when either A or B, but not both, are true.

anonymous · Answer

Exactly!