{"@context":"https://schema.org/","@type":"Quiz","name":"

$A \\cup B=U$ is only true, when

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"NET"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"NET","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/aub-u-is-only-true-when"}],"about":{"@type":"Thing","name":"NET, NUST Entry Test, Mathematics, Quiz"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["NET","NUST Entry Test","Mathematics","Quiz"],"name":"

$A \\cup B=U$ is only true, when

","comment":{"@type":"Comment","text":"

We are given:

$A \\cup B = U \\quad\\quad\\quad\\quad\\quad...~(1)$

Here $U$ is the universal set that contains all the elements.

Option C states that $A'=B$

The complement of set $A$ is denoted as $A'$ and it contains all the elements present in the universal set except the elements of set $A$.

$A'=U-A$

Substitute $A'=B$ in $(1)$

$A \\cup A'=U$

This is true as the union of a set and its complement is equal to the universal set.

"},"encodingFormat":"text/markdown","text":"

$A \\cup B=U$ is only true, when

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$A=B$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$A\\subseteq B$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

None of the above

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$A'=B$

","comment":{"@type":"Comment","text":"

We are given:

$A \\cup B = U \\quad\\quad\\quad\\quad\\quad...~(1)$

Here $U$ is the universal set that contains all the elements.

Option C states that $A'=B$

The complement of set $A$ is denoted as $A'$ and it contains all the elements present in the universal set except the elements of set $A$.

$A'=U-A$

Substitute $A'=B$ in $(1)$

$A \\cup A'=U$

This is true as the union of a set and its complement is equal to the universal set.

"},"answerExplanation":{"@type":"Comment","text":"

We are given:

$A \\cup B = U \\quad\\quad\\quad\\quad\\quad...~(1)$

Here $U$ is the universal set that contains all the elements.

Option C states that $A'=B$

The complement of set $A$ is denoted as $A'$ and it contains all the elements present in the universal set except the elements of set $A$.

$A'=U-A$

Substitute $A'=B$ in $(1)$

$A \\cup A'=U$

This is true as the union of a set and its complement is equal to the universal set.

"}}},"url":"https://classnotes.xyz/mcqs/aub-u-is-only-true-when"}

$A \cup B=U$ is only true, when