Complement of a set, Law of Complement, Property of Complement - Practice Questions & MCQ

Let $U$ be the universal set and $A$ is a subset of $U$. Then the complement of $A$ is the set of all elements of $U$ which are not the elements of $A$.

Symbolically, we use $\mathrm{A}^{\prime}$ or $\mathrm{A}^{\mathrm{C}}$ to denote the complement of A with respect to U .
$A^{\prime}=\{x: x \in U$ and $x \notin A\}$. Obviously, $A^{\prime}=U-A$

Properties of Compliment

$A \cup A^{\prime}=U$
$\mathrm{A} \cap \mathrm{A}^{\prime}=\varphi$
$\left(\mathrm{A}^{\prime}\right)^{\prime}=\mathrm{A}$
$U^{\prime}=\varphi$ and $\varphi^{\prime}=U$
$A-B=A \cap B^{\prime}$