"The result of the toss is head if and only if I am telling the truth"
say type1 people telling truth
putting negation
The result of toss is not head if and only if I am not telling truth // now is this statement false ? No it is true . right?
So, result must head as Type1 people is telling truth
Now, type2 people is telling lie
but he also telling "The result of the toss is head if and only if I am telling the truth"
Now, our question is how the same statement could be FALSE?
here is the logic
The result of the toss is head = P
I am telling the truth= Q
According to lie teller P =TRUE (means the result is true)
Q=FALSE (as FALSE teller must speaking FALSE )
Now according to the statement P⟷Q = (P⟶Q) ⋀(Q⟶P).....................(i)
Now, for being it false either P⟶ Q = FALSE or Q⟶P is FALSE. right?
Now, P⟶Q means (~P ⋁Q) i.e. The result of the toss is not head or I am telling truth = False ⋁ False = FALSE // here Q is false as he is a lie teller
Q⟶P means(~Q⋁P) i.e. I am telling FALSE or the result of the toss is head = TRUE⋁TRUE = TRUE
Now, putting it in equation (i) we get FALSE⋀TRUE =FALSE
So, the lier also telling same statement , but he is lying.
So, the result is head :)