I have following facts
No set is an element of itself.
xis a subset of a set
yiff every element of
xis an the element of
Something is an element of the union of two sets
yiff it is an element of
xor an element of
I have represented the above fact in fol as follows
- $\forall x \neg Elt(x,x)$
- $\forall x \forall y \forall z \ Sub(x,y) \equiv (Elt(z,x) \rightarrow Elt(z,y))$
- $\forall x \forall y \forall z \ Elt(z,u(x,y)) \equiv (Elt(z,x) \vee Elt(z,y))$
We called the above fact as
As nonlogical symbols, use
Sub(x, y) to mean "
x is a subset of
Elt(e, x) to mean "
e is an element of
u(x, y) to mean "the union of
I am not able to interpret following statement in FOL.
Show using logical interpretations that
Tdoes not entail that the union of
yis equal to the union of
Abe any set. Show using logical interpretations that
Tentails that there is a set
zsuch that the union of
zis a subset of
Question from Knowledge Representation and Reasoning. To understand Knowledge Representation and Reasoning, I am trying to solve the problem set of that book.