Exercises
[0GM]Given the sets \(A, \, B\subseteq {\mathbb {R}}\), determine the relations between the following pairs of sets
\begin{align*} \overline{A\cup B} \qquad \qquad \text{ \text{and}~ }& \, \qquad \qquad \overline{A}\cup \overline{B}\, ,\\ \overline{A\cap B} \qquad \qquad \text{ \text{and}~ }& \, \qquad \qquad \overline{A}\cap \overline{B}\, ,\\ {{({A\cup B})}^\circ } \qquad \qquad \text{ \text{and}~ }& \, \qquad \qquad {{A}^\circ } \cup {{B}^\circ }\, , \\ {{({A\cap B})}^\circ } \qquad \qquad \text{ \text{and}~ }& \, \qquad \qquad {{A}^\circ } \cap {{B}^\circ }\, . \end{align*}[ [0GN]]
Solution 1