Let \(\mathrm{f}:[0,1] \rightarrow \mathbb{R}\) and \(\mathrm{g}:[0,1] \rightarrow \mathbb{R}\) be defined as follows :
\(\left.\begin{array}{rl}
f(x) & =1 \text { if } x \text { is rational } \\
& =0 \text { if } x \text { is irrational }
\end{array}\right] \text { and }\)
\(\left.\begin{array}{rl}
g(x) & =0 \text { if } x \text { is rational } \\
& =1 \text { if } x \text { is irrational }
\end{array}\right] \text { then }\)

1. A \(f\) and \(g\) are continuous at the point \(x=\frac{1}{2}\)
2. B \(\mathrm{f}+\mathrm{g}\) is continuous at the point \(\mathrm{x}=\frac{2}{3}\) but f and g are discontinuous at \(\mathrm{x}=\frac{2}{3}\)
3. C \(f(x) \cdot g(x)\gt0\) for some points \(x \in(0,1)\)
4. D \(\mathrm{f}+\mathrm{g}\) is not differentiable at the point \(\mathrm{x}=\frac{3}{4}\)