Translate the following into everyday English. Note that everyday English does not use variables.
In the following wfs $A^1(x)$ means $x$ is a person, $A^2(x,y)$ means $x$ hates $y$.
$i)\exists x (A^1(x)\land\forall y (A^1(y)\to A^2(x,y)))$
$ii)\forall x(A^1(x)\to\forall y(A^1(y)\to A^2(x,y)))$
$iii)\exists x (A^1(x)\land\forall y(A^1(y)\to(A^2(x,y)\leftrightarrow A^2(y,y))))$
I did i)
i) For every person, there exist another person such that the second hates the first person.
Is it correct?
Also note that I first translate the proposition inside $\forall y (A^1(y)\to A^2(x,y))$
How do I translate $ii)$ and $iii)$?
This is very difficult help please
Your (i) is incorrect.
Try writing out the definitions of the symbols $\exists$,$\forall$,$\implies$, $A^1$,$A^2$ then simplifying the English.
(i) reads "there exists $x$ such that $x$ is a person and for every $y$, $y$ being a person implies $x$ hates $y$.
More simply this is just "some dude $x$ hates all people"
Try the other two by first writing out the literal meanings then simplifying.