$X \sim N(0,1)$ and $c>0$ such that $ \begin{equation} \nonumber Y =\left\{ \begin{array}{l l} X & \quad |X|<c \\ & \quad \\ -X & \quad |X| \geq c \end{array} \right. \end{equation}$
so $Y$ is normal distributed beacuse $P(Y\leq y) = P(X\leq y)+P(X > y)= \int_{-\infty}^{y}\frac{1}{\sqrt{2 \pi}} e^{-\frac{u^2}{2}}du+\int_{y}^{\infty}\frac{1}{\sqrt{2 \pi}} e^{-\frac{u^2}{2}}du=\int_{-\infty}^{\infty}\frac{1}{\sqrt{2 \pi}} e^{-\frac{u^2}{2}}du $
but I dont understand how can I continiue from here to show that $(X,Y)$ is not normal distributed