Class 11 Mathematics - Sets - Operations on Sets (Union, Intersection, Difference) Hard Quiz

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यदि \(A\) और \(B\) वेन आरेख में ओवरलैप करने वाले दो वृत्त हैं, तो \(A - (A\cap B)\) किसके समान होगा?

If \(A\) and \(B\) are two overlapping circles in a Venn diagram, what is \(A - (A\cap B)\) equal to?

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Correct Answer

A. \(A\setminus B\)

Explanation

Simple Explanation

\(A\cap B\) में वे तत्व होते हैं जो \(A\) और \(B\) दोनों में हैं। इसलिए \(A-(A\cap B)\) में \(A\) के वे तत्व बचते हैं जो \(B\) में नहीं हैं। यह ठीक \(A\setminus B\) है। विकल्प \(B\setminus A\) गलत है, क्योंकि वह \(B\) के उन तत्वों को दर्शाता है जो \(A\) में नहीं हैं। परीक्षा सुझाव: वेन आरेख में \(A\) के उस हिस्से को देखें जो साझा क्षेत्र के बाहर है। / The intersection \(A\cap B\) contains elements that belong to both \(A\) and \(B\). Therefore, removing \(A\cap B\) from \(A\) leaves the elements that are in \(A\) but not in \(B\), which is exactly \(A\setminus B\). The distractor \(B\setminus A\) is incorrect because it represents elements in \(B\) but not in \(A\). Exam tip: In the Venn diagram, identify the part of \(A\) outside the overlapping region.

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