E open set U closed set Is the result open closed neither E

Solution

The union can be either open or closed or neither of them as depending upon the the sets taken.

Let us consider the examples

1. Let set A = (1,5) and set B = [0,6]. Then AUB = [0,6] which is a closed set.

2. Let set A = (1,5) and set B = [2,4]. Then AUB = (1,5) which is an open set.

3. Let set A = (1,5) and set B = [0,4]. Then AUB = [0,5) which neither open nor closed.