Prove $\left( A ^{\prime}\right)^{\prime}= A$ for an empty set $A$.
✓
Answer
Here, $\quad A =\{ \}$ Let $x$ be an universal set, then $\begin{array}{l}A^{\prime}=\text { The set of all elements of set } U \text { which are not in } A \\=x(\because \text { no element of } U \text { is in } A)\end{array}$ Now, $\quad\left( A ^{\prime}\right)^{\prime}=x^{\prime}$ $=$ Set of those elements of $x$ which are not in $x$ $=\{ \} \quad(\because$ no element of $x$ is in $x)$ $= A$ $\therefore \quad\left( A ^{\prime}\right)^{\prime}= A$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.