Translate to First Order Logic I have this two sentences:


*

*All men love the woman to whom they are married.

*No woman loves a man who does not respect all women.


and in the exercise they are translated to First Order Logic as follows:
$\forall{x}\text{ }male(x) \land \exists y [female(y) \land married(x, y)\to loves(x, y)]$
$\lnot\exists{x}\text{ }female(x) \land \forall y\forall z [female(z) \land \lnot{respect(y, z)}\land loves(x, y)]$
but I would translate them in this way:
$\forall{x}\text{ }male(x) \to \exists y [(female(y) \land married(x, y))\to loves(x, y)]$
$\forall{x}\text{ }female(x) \to \forall y\forall z [(
female(z) \to(\lnot{respect(y, z)}\to\lnot loves(x, y))]$
Where am I wrong?
I would appreciate your help.
Thanls in advance
 A: Well, the provided answers are certainly not correct. 
I see that for both of the you added some parentheses to help disambiguate, which is good.  Some books use a 'priority' system to say that something like $P \land Q \to R$ will always mean $(P \land Q) \to R$ (so we can't really 'fault' the book on that one), but I think it is good idea to use explicit parentheses the way you do. Good!
Also, for both answers, your intuition that on several occasions we need to use a $\to$ rather than a $\land$ is correct .... for example, the first provided answer effectively saying that everyone is male! Again: good for you to realize the book's mistake!
But: as Mauro points out, we really need parentheses to indicate the cope of thew quantifier, otherwise the $x$ ends up being free. So, at the very least you want:
$\forall{x}\text{ }\big( male(x) \to \exists y [(female(y) \land married(x, y))\to loves(x, y)]\big)$
OK, but that still isn't right! Indeed, there is a major problem with your translation as well!
To see this, suppose that for $y$ we take something from the domain that is not female (presumably $x$ itself!). Then: it is false that $female(y)$, and hence false that $female(y) \land married(x, y)$, and hence true that $(female(y) \land married(x, y))\to loves(x, y)$. 
Hence, of course the whole $\exists y [(female(y) \land married(x, y))\to loves(x, y)]$ is true: just pick something that is not female!  ... but that of course says nothing of interest about men loving the woman they are married to! Thus we say that $\exists y [(female(y) \land married(x, y))\to loves(x, y)]$ is 'vacuously true'. ... and it's clearly not what we want.
OK, so how about:
$\forall{x}\text{ }\big( male(x) \to \forall y [(female(y) \land married(x, y))\to loves(x, y)]\big)$
Well, now at least all men will love whichever woman they are married to ... so that's a whole lot closer to what you want ... and probably acceptable as an answer. ... However ... the statement does not rule out that the man is married to more than one woman. So, to capture that the man loves the woman they are married to (if they are married to a woman at all), we could do this:
$\forall{x}\text{ }\big( male(x) \to \forall y \forall z[(female(y) \land female(z) \land married(x, y) \land married(x, z))\to (y=z \land loves(x, y))]\big)$
For the second one, again we need parentheses for the scope of $x$:
$\forall{x}\text{ }\big( female(x) \to \forall y\forall z [(female(z) \to\lnot{respect(y, z)})\to \neg loves(x, y)]\big)$
But we have a more serious  problem ... where is the reference to $y$ being male?!
OK, so at the very least we need something like:
$\forall{x}\text{ }\big ( female(x) \to \forall y\forall z [(male(y) \land (female(z) \to\lnot{respect(y, z))})\to \neg loves(x, y)]\big)$
But this isn't right either!  This statement claims something about any $y$ and $z$.  OK, so pick for $z$ something that is not female. Then as with the previous sentence, $female(z) \to\lnot respect(y, z)$ becomes vacuously true, and therefore, it would follow that $\neg loves(x, y)$ ... even if the man $y$ does respect all women!
OK, so we need something more like:
$\forall{x}\text{ }\big ( female(x) \to \forall y [(male(y) \land \forall z (female(z) \to\lnot{respect(y, z))})\to \neg loves(x, y)]\big)$
But there is another problem yet! This statement is saying that $y$ is a man who does not respect any women at all .... and I interpret the English sentence as saying that it is about men who don't respect all women (that is, as soon as there is at least one woman that this man does not respect, then $x$ will not love that man). So, we need to change this to:
$\forall{x}\text{ }\big ( female(x) \to \forall y [(male(y) \land \neg \forall z(female(z) \to {respect(y, z))})\to \neg loves(x, y)]\big)$
Another option is what you do in your second attempt:
$\forall x female (x)\to\forall y \forall z[male(y)\to(female(z)\to(\lnot respect(y,z)\to \lnot love(x,z)))]$
Now again, we need to add parentheses for the scope of $x$:
$\forall x \big ( female (x)\to\forall y \forall z[male(y)\to(female(z)\to(\lnot respect(y,z)\to \lnot love(x,z)))]\big)$
And another thing we can do is to make this into the equivalent:
$\forall x \big ( female (x)\to\forall y \forall z[(male(y)\land female(z))\to(\lnot respect(y,z)\to \lnot love(x,z)))]\big)$
.. which looks very much what you had originally, but the change in parentheses makes all the difference!
Finally, to show that my answer and this second answer are equivalent:
$\forall{x}\text{ }\big ( female(x) \to \forall y [(male(y) \land \neg \forall z(female(z) \to {respect(y, z))})\to \neg loves(x, y)]\big) \Leftrightarrow$
$\forall{x}\text{ }\big ( female(x) \to \forall y [male(y) \to (\neg \forall z(female(z) \to {respect(y, z))}\to \neg loves(x, y))]\big) \Leftrightarrow$
$\forall{x}\text{ }\big ( female(x) \to \forall y [male(y) \to (loves(x, y) \to \forall z(female(z) \to {respect(y, z))})]\big) \Leftrightarrow$
$\forall{x}\text{ }\big ( female(x) \to \forall y [male(y) \to \forall z (loves(x, y) \to (female(z) \to {respect(y, z))})]\big) \Leftrightarrow$
$\forall{x}\text{ }\big ( female(x) \to \forall y \forall z[male(y) \to (loves(x, y) \to (female(z) \to {respect(y, z))})]\big) \Leftrightarrow$
$\forall{x}\text{ }\big ( female(x) \to \forall y \forall z[male(y) \to ((loves(x, y) \land female(z)) \to {respect(y, z)})]\big) \Leftrightarrow$
$\forall{x}\text{ }\big ( female(x) \to \forall y \forall z[male(y) \to (( female(z) \land loves(x, y)) \to {respect(y, z)})]\big) \Leftrightarrow$
$\forall{x}\text{ }\big ( female(x) \to \forall y \forall z[male(y) \to ( female(z) \to (loves(x, y) \to {respect(y, z)}))]\big) \Leftrightarrow$
$\forall{x}\text{ }\big ( female(x) \to \forall y \forall z[male(y) \to ( female(z) \to (\neg {respect(y, z)} \to \neg loves(x, y) ))]\big) $
A: Thank you so much @Bram28.
Let's start with the first sentence: I have understood what you said, just one question, Is there a way to realize the sentence using the existential quantifier instead of the universal quantifier?
for the seconde sentence, adding the man reference I've done as follows
$\forall x female (x)\to\forall y \forall z[male(y)\to(female(z)\to(\lnot respect(y,z)\to \lnot love(x,y)))]$
Is that right?
Thank you :)
A: The phrasing "the woman to whom they are married" seems to assume as a given that every man is married to one unique woman. Expressing that most naturally in first-order logic calls for a function letter rather than a relation, so I would write
$$ \forall m.\,\text{man}(m) \to \text{loves}(m,\text{wife}(m)) $$
