"Everyone in the world love themselves"
"Someone loves their own self"
x, y are everyone in the world
1) ∀x∃y(love(x, y) /\ (x=y))
2)∃x∃y(love(x, y) /\ (x=y))
I'm thinking along the lines of "everyone/someone loves someone, and that someone is themselves"
am i correct? and can those two be shortened?
thank you
If the function love$(x,y)$ is defined as $x$ loves $y$ and that the relation $x=y$ mean that $x$ is the same person as $y$, then (1) translate to "for every one in the world, there exist someone such that $x$ loves $y$ and that $x$ is the same person as $y$ ". The second one is "there exists two person in the world such that they loves each other and they are the same".
If you are trying to say "Everyone in the world love themselves", then I would go with $\forall x(\text{love}(x,x))$. And for "Someone loves their own self", $\exists x(\text{love}(x,x))$.
Note that this is more or less subjective and depend on how the function love$(x,y)$ is defined.
Hope that help!