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Quantified Propositions

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1. Homework Statement

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. Homework 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)##.
 

Stephen Tashi

Science Advisor
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Can you see if I'm on the right track here?
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)) )##
 
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No it's not very picky about the parenthesis.

Thanks, though!
 

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