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

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Home Questions Q7G637CH3X

Target Exam

CUET

Subject

Mathematics

Chapter

Sets

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:

The correct answer is Option (2) → $B = C$

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,

$A∪B = A∪C$

$⇒(A∪B)∩B=(A∪C)∩B$

$⇒B=(A∩B)∪(B∩C)$

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