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PART - 1 CH - 1 Sets — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSPART - 1 CH - 1 Sets2 Marks
Question
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 $x)$
$= A$
$\therefore \quad\left( A ^{\prime}\right)^{\prime}= A$

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