{ x l x e R and 0 < x < 2}
{1,2}
The book says these two sets aren't equal but I don't understand why not.
The set $\displaystyle \left\{ {x:x \in \Re \wedge 0 < x \leqslant 2} \right\}$ is the set of all real numbers that a greater than 0 but less than or equal to 2.
Whereas, $\displaystyle \left\{ {0,2} \right\}$ is a set with only two elements, 0 & 2.
Do you see why it is impossible that they could be equal?