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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
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14 Questions around this concept.
Solve by difficulty
Let be defined by
for
then
is.
If then range of
is.
Which of the following relation represent the properties of the complement set?
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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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