If $\(0<x<\frac{1}{2}\) ; \(\frac{1}{2}<y<1 \Rightarrow x<\frac{1}{2}\)$ and $\(y>\frac{1}{2} \Rightarrow \frac{1}{x}>2\)$ and $\(\frac{1}{y}<2\)$

Compare these values with the given options, to note that options $A, B$ are true and option $C$ is not true. Since $\(x<\frac{1}{2}\)$ and $\(y>\frac{1}{2}\)$, for some values of $\(x\)$ and $\(y, x y<\frac{1}{2}\)$ and $\(x+y=1\)$.

Hence the options $D$ and $E$ are true.

Since the maximum value of $y$ is less than 1 and the maximum value of $x$ is less than $\(\frac{1}{2}\)$, options $F$ and $G$ are not true. Thus, the correct options are $A, B, D$ and $E$.