JEE Main 2009MathematicsSets And RelationsVenn DiagrammediumMCQ

JEE Main 2009 — Sets And Relations Question with Solution

From: AIEEE 2009

Question

If and are three sets such that and , then :

Choose an option

Show full solutionCorrect option: B
Correct answer
B

Step-by-step explanation

From the given conditions, we have :

  1. A ∩ B = A ∩ C : The intersection of set A with set B is the same as the intersection of set A with set C. This indicates that all elements common to A and B are also common to A and C, and vice versa.


  2. A ∪ B = A ∪ C : The union of set A with set B is the same as the union of set A with set C. This indicates that all elements in A, B, and C are the same.

From these two conditions, we can infer that set B is equal to set C because every element of B is also an element of C and vice versa. Hence, Option B : B = C is the correct answer.

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About this question

This is a previous-year question from JEE Main 2009, covering the Sets And Relations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.