There exists x∈Σ* such that for every y∈L(M),xy∉L(M)
Let P(y) denote that y∈L(M)
And Q(x,y) denote that xy∉L(M) where x∈Σ*
So this statement can be written like:
∃x,∀y P(y)⋀Q(x,y)
∃x,∀y P(y)⋀Q(x,y) = {P(y1)⋀Q(x1,y1) ⋀ P(y2)⋀Q(x1,y2)⋀.....⋀ P(yn)⋀Q(x1,yn) } ⋁
{P(y1)⋀Q(x2,y1) ⋀ P(y2)⋀Q(x2,y2)⋀.....⋀ P(yn)⋀Q(x2,yn) }⋁
{P(y1)⋀Q(xm,y1) ⋀ P(y2)⋀Q(xm,y2)⋀.....⋀ P(yn)⋀Q(xm,yn) }
where yi belongs to L(M) and xj belongs to Σ*.
Now if L(M)= { } is Tyes then this predicate logic should be valid.
@Arjun Sir please help me proceed..I am stuck! And if all what i wrote is wrong then please correct me..