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

    Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

    Quick Facts

    • 20 Questions around this concept.

    Solve by difficulty

    QuestionEASY

    $\left(A^{\prime}\right)^{\prime}=$

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    $A \cap A^{\prime}=$

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    $U^{\prime}=$

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    Write A' where $A=\{x:x\in I,-3<x<3\}$

    $U=\{x:x\in I,-10<x<10\}$

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    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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    Complement of a set, Law of Complement, Property of Complement

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    Intersection of Set, Properties of Intersection
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    Complement of a set, Law of Complement, Property of Complement
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