What is the solution set of {x | x < 2} ∪ {x | x ≥ 2}

The union of two sets is defined as all elements that are members of both sets.

The first set evaluuates to (...,...,...-2,-1,0,1) and the second eveluates to (2,3,4,5,...,...).

There are no elements that belong to both sets so the solution is the empty set. {∅}

Another way is to think about it in words: "What number(s) are less that 2 and also equal to to greater than 2?" Clearly there is no number that fits both of those.