If A, B, C be three sets such that $A&cu

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If A, B, C be three sets such that $A∪B=A∪C$ and $A∩B=A∩C$, then

Options:

$A =B$

$B=C$

$A=C$

$A=B=C$

Correct Answer:

$B=C$

Explanation:

We have,

$A∪B=A∪C$

$⇒(A∪B)∩C=(A∪C)∩C$

$⇒(A∩C)∪(B∩C)=C$

$⇒(A∩B)∪(B∩C)=C$ $[∵A∩C=A∩B]$ ..(i)

Again,

$A∪B=A∪C$

$⇒(A∪B)∩B=(A∪C)∩B$

$⇒B=(A∩B)∪(B∩C)$ ...(ii)

From (i) and (ii), we get $B = C$.