1.
Let Q\mathbb{Q} be the set of all rational numbers in [0,1][0, 1] and f:[0,1][0,1]f : [0, 1] \to [0, 1] be defined by f(x)={xfor xQ1xfor xQf(x) = \begin{cases} x & \text{for } x \in \mathbb{Q} \\ 1-x & \text{for } x \notin \mathbb{Q} \end{cases}. Then, the set S={x[0,1]:(ff)(x)=x}S = \{x \in [0, 1] : (f \circ f)(x) = x\} is equal to