Let f:[0,3] → R be defined by f(x)= min {x-[x], 1+[x]-x} where [x] is the greatest integer less than or equal to x. Let P denote the set containing…

Let $\displaystyle f:[0,3] \rightarrow \mathbb{R}$ be defined by $$f(x)=\min \{x-[x], 1+[x]-x\} $$ where $\displaystyle [x]$ is the greatest integer less than or equal to $\displaystyle x$. Let P denote the set containing all $\displaystyle x \in[0,3]$ where $\displaystyle f$ is discontinuous, and Q denote the set containing all $\displaystyle x \in(0,3)$ where $\displaystyle f$ is not differentiable. Then the sum of number of elements in P and Q is equal to \_\_\_\_.