Mathematical Logic Problem? I'm trying to solve this mathematical logic problem, can someone please at least give me a tip on how to approach this problem?

The square of any positive real number is a positive real number.
Write down the,

*

*statement in symbolic form

*the converse of the statement in symbolic form

*the negation of the statement in symbolic form and sentence form


Thank you.
 A: Hint 1: Try thinking of the given sentence as:

For any $x$, if $x$ is a positive real number, then $x^2$ is a positive real number.

Hint 2: Suppose that we have a statement of the form:
$$
\text{If $p$ is true, then $q$ is true.}\tag{1}
$$
Then the converse of $(1)$ is of the form:
$$
\text{If $q$ is true, then $p$ is true.}
$$
Furthermore, the negation of $(1)$ is of the form:
$$
\text{$p$ is true but $q$ is false.}
$$
Hint 3: Recall that negations of universally quantified predicates turn into existentially quantified (negated) predicates. More precisely:
$$
\neg[\forall x,~ P(x)] \qquad\text{is equivalent to}\qquad \exists x ~~\neg P(x)
$$
A: Hint:  If you define $P(x)$ (or whatever form you use) to mean "$x$ is a positive real number", the first becomes $P(x) \implies P(x^2)$  How do you write the converse of an implication?  To write the negation, you can just precede it by $\lnot$, but you may be expected to turn it into a conjuction.  How can an implication be false?
A: First translate the sentence to 'first order English' language:

  
*
  
*For all positive real number, its square is positive.
  
*For all real number $x$, if $x$ is positive, then $x^2$ is positive.
  

