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Complement of a set, Law of Complement, Property of Complement - Practice Questions & MCQ
Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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20 Questions around this concept.
Solve by difficulty
$\left(A^{\prime}\right)^{\prime}=$
$A \cap A^{\prime}=$
$U^{\prime}=$
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Write A' where $A=\{x:x\in I,-3<x<3\}$
$U=\{x:x\in I,-10<x<10\}$
Concepts Covered - 1
Complement of a set, Law of Complement, Property of Complement
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 $\varphi^{\prime}=U$
$A-B=A \cap B^{\prime}$
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