4.2 Consider the following predicate symbols with which we associate the following meanings:
$B(x)$ represents " $x$ is a bird"
$W(x)$ represents " $x$ is a worm"
$E(x, y)$ represents " $x$ eats $y$ "
Provide a predicate formula for each of the following statements:
(i) "Every bird east every worm"
(ii) "Some birds do not eat some worms"
(iii) "No bird is eaten by a worm"
(iv) "Some worms do not get eaten by birds"
(v) "Worms are only eaten by birds"
For part (iii) their solution is:
$\neg \exists x \exists y(B(x) \wedge W(y) \wedge E(y, x))$
But my solution is:
$\forall x\forall y(B(x) \wedge W(y) \rightarrow \neg E(y,x))$
For part (iv) their solution is:
$\exists x(W(x) \wedge \forall y(B(y) \rightarrow \neg E(y, x)))$
But my solution is:
$\forall y \exists x(B(y) \wedge W(x) \rightarrow \neg E(y,x))$
For part (v) their solution is:
$\forall x(W(x) \rightarrow \forall y(E(y, x) \rightarrow B(y)))$
But my solution is:
$\forall x \forall y(\neg B(y) \wedge W(x) \rightarrow \neg E(y,x))$
Your answer to (iii) is logically equivalent to the given one, indeed : $$ \begin{eqnarray}[cc]\neg \exists x \exists y(B(x) \wedge W(y) \wedge E(y, x)) & \equiv \\ \forall x \neg \exists y(B(x) \wedge W(y) \wedge E(y, x)) & \equiv \\ \forall x \forall y \neg (B(x) \wedge W(y) \wedge E(y, x)) & \equiv \\ \forall x \forall y \neg \big(B(x) \wedge W(y) \big) \vee \neg E(y, x) & \equiv \\ \forall x\forall y(\big( B(x) \wedge W(y)\big) \rightarrow \neg E(y,x)) \end{eqnarray}$$
Your solution lacks those extra braces.
Your answer to (iv) is wrong : what you wrote,
Readily means "For every bird there is a worm that does not get eaten by this bird.".
It is possible, however, that the worm(s) that this particular bird failed to eat get swallowed by some other bird that wants its share!
Your answer to (v) is once again logically equivalent to the given one, but I'm too lazy to show why.