I have to convert the given predicates to English sentences. I have tried from my side but I am very confused (as there can be many forms to represent a statement and also that my English statement might be wrong). Here are the predicates and English statements. Please tell me if there can be a better answer for any of these?
$\forall x\exists y R(x,y)$
For every $x$ there is at least one $y$ such that $R(x,y)$
$\exists x\forall y R(x,y)$
For every $x$ there is a single $y$ such that $R(x,y)$
EDIT:
There is an x $x$ for which there is a single $y$ such that $R(x,y)$
$\forall x(\neg Qx)$
For every $x$ $Q(x)$ is false; or $Q(x)$ is false for every $x$
$\exists y(\neg P(y))$
There is at least one $y$ for which $P(y)$ is false.
Please help me out. Thanks.