Need help with first order logic

Question

I'm trying to understand first-order-logic and have this simple question.

Given the following predicates:

$Thing(t)$, which states that $t$ is a thing;

$Word(w)$, which states that $w$ is a word; and

$HurtsYouMoreThan(x,y)$, which states that $x$ hurts you more than $y$,

I need to create a first-order-logic statement that says "There is nothing that hurts you more than words do.

Answer 1

It will help to re-word it:

No thing hurts more than words do.

In other words:

For all $w$ and for all $t$, if $w$ is a word and $t$ is a thing, it is not true that $t$ hurts you more than $w$.

$$(\forall{w})(\forall{t}){(\operatorname{word}(w)\land\operatorname{thing}(t))\to\lnot\operatorname{HurtsYouMoreThan}(t,w)}$$

Answer 2

Revised to match new question.

HINT: There is nothing that hurts you more than words do can be understood as follows:

If $x$ is anything other than a word, and $y$ is any word, then $x$ does not hurt you more than $y$ does.

From here the translation into a sentence of first-order logic using your three predicates should be pretty straightforward. Note that you will have a couple of quantifiers.

Answer 3

Hint: If I'm interpreting the given sentence correctly, you should be able to think about this as a sentence more like $$\text{Given any thing $$X which isn't a word and any thing $Y$ which is a word, ...}$$