Propostional Functions

Question

Let $P$ stand for the set of people and let $p \in P$. $C(p)$ is a propositional function that is true when person $p$ plays cricket; $R(p)$ is a propositional function that is true when $p$ plays rugby; and $F(p)$ is true when $p$ plays football. Formalise the following statements:

1) Someone plays football and rugby.

2) No-one[sic] plays rugby and cricket.

3) If someone plays cricket, then that person also plays either football or rugby.

4) Everyone either plays cricket and football, or they play no sport at all.

Can someone please give me answers to this so that I can see if I am right or not? And if possible explain like one of the questions how they got there?

Cant post on here my answer as i cant find symbols and notations

if someone could provide the answers it would be helpful, not that I haven't put the effort in, because obviously I am going to do the exam and there is no point in just getting the answers, I just need to see if I am right, will take too much time having to add it in on a computer, much appreciated.

I am new to this so I apologise.

don't just post a link. This doesn't show any of your effort, you've surely invested already... — draks ..., Aug 11 '13 at 21:45
Go here http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference — draks ..., Aug 11 '13 at 21:47
Hmm, seems complicated, if someone could provide the answers it would be helpful, not that I haven't put the effort in, because obviously I am going to do the exam and there is no point in just getting the answers, I just need to see if I am right, will take too much time having to add it in on a computer, much appreciated — Jay, Aug 11 '13 at 21:50

score 2 · Accepted Answer · answered Aug 11 '13 at 22:26

I'm assuming you're getting your chops busted because you're asking for others to put in effort to answer your question but you're unwilling to put in the effort to ask your question in a way that is helpful. Rather than being able to type an answer while looking at the question, I have to have another window open that I'm tabbing back and forth between. So, for others, here is the original question:

Let $P$ stand for the set of people and let $p \in P$. $C(p)$ is a propositional function that is true when person $p$ plays cricket; $R(p)$ is a propositional function that is true when $p$ plays rugby; and $F(p)$ is true when $p$ plays football. Formalise the following statements:

1) Someone plays football and rugby.

2) No-one[sic] plays rugby and cricket.

3) If someone plays cricket, then that person also plays either football or rugby.

4) Everyone either plays cricket and football, or they play no sport at all.

That said, the following is a way to answer the questions, but certainly not the only way (there are certainly other answers that may look different but are logically equivalent). Also, I don't like my answer to #4; I might have to rethink it.

$\exists p \in P: F(p) \wedge R(p)$
$\forall p \in P: \neg (R(p) \wedge C(p)$
$\forall p \in P: C(p) \implies F(p) \vee R(p)$
$\forall p \in P: (C(p) \wedge F(p)) \vee \neg(C(p) \vee R(p) \vee F(p))$

Sorry i really do apologize for not giving enough detail in my question, it's just that I am new to this and can't see how the symbols are added, now I can use these symbols by copying and pasting next time, yeah the fourth one i have a different answer, I probably did it wrong, going to try do it again. — Jay, Aug 12 '13 at 12:58

Propostional Functions

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