# Quantified Propositions

1. Feb 18, 2015

### spaghetti3451

1. The problem statement, all variables and given/known data

I've been trying to translate the following sentences into quantified propositions by making sure I state all propositional functions that I use and any assumptions that I make.

Can you see if I'm on the right track here?

2. Relevant equations

3. The attempt at a solution

1. All engineers are good with computers.

Let $E(x)$ be '$x$ is an engineer' and $C(x)$ be '$x$ is good with computers,'
where the domain of $x$ is all people in the world.

Then, $\forall x\ E(x) \rightarrow C(x)$.

2. Some mathematicians also like poetry.

Let $M(x)$ be '$x$ is a mathematician' and $P(x)$ be '$x$ also likes poetry,'
where the domain of $x$ is all people in the world.

Then, $\exists x\ M(x) \land P(x)$.

3. There are no writers who do not like reading books.

Let $W(x)$ be '$x$ is a writer' and $B(x)$ be '$x$ likes reading books,'
where the domain of '$x$ is all people in the world.

Then, $\neg\ \exists x\ W(x) \land \neg B(x)$.

4. Not every athlete is famous.

Let $A(x)$ be '$x$ is an athlete' and $F(x)$ be '$x$ is famous,'
where the domain of $x$ is all people in the world.

Then, $\neg \forall x\ A(x) \rightarrow F(x)$.

5. Only scientists properly value civilisation.

Let $S(x)$ be '$x$ is a scientist' and $C(x)$ be '$x$ properly values civilisation,'
where the domain of $x$ is all people in the world.

Then, $\forall x\ C(x) \rightarrow S(x)$.

2. Feb 19, 2015

### Stephen Tashi

You are on the right track. Is your course material particular about using parentheses and brackets?

For example,

$\neg \forall x\ A(x) \rightarrow F(x)$.

could be written as:

$\neg (\forall x (\ A(x) \rightarrow F(x)) )$

3. Feb 26, 2015

### spaghetti3451

No it's not very picky about the parenthesis.

Thanks, though!