The given statement is:

"Square of a negative real number is positive."

We need to negate this statement, and we have the following options.

Let's break down the original statement:

1. Original statement in logical terms: "For all $x$, if $x$ is less than 0, then $x^2 > 0$" (since the square of any real number is positive).
   • In symbolic form: $\forall x ((x < 0) \to (x^2 > 0))$.

Negation of the statement:

The negation of the statement "For all $x$, if $x < 0$, then $x^2 > 0$" would be "There exists some $x$ such that $x < 0$ and $x^2 \leq 0$" (i.e., the square of some negative number is non-positive, meaning it is 0 or negative).

This leads us to the option that matches the negation:

• Option C: $\exists x ((x < 0) \land (x^2 \leq 0))$

This correctly represents the negation of the original statement. Therefore, the correct answer is:

C) $\exists x ((x < 0) \land (x^2 \leq 0))$.

Would you like more details on the logical steps involved? Here are five related questions you can explore:

1. What are the rules for negating "for all" ($\forall$) and "there exists" ($\exists$) quantifiers?
2. How do implications ($\to$) work in logical statements?
3. Why does the square of a real number always result in a non-negative number?
4. What are the properties of real numbers under squaring?
5. How do logical conjunction ($\land$) and disjunction ($\lor$) work in truth tables?

Tip: When negating a statement involving "for all" ($\forall$), it turns into "there exists" ($\exists$), and the internal logical condition flips accordingly.