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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let A and B be sets. $A\cap X=B\cap X=\phi$ and $A\cup X=B\cup X$ for some set X, relation between A & B
Solution
Given: \(A\cap X=\varnothing,\; B\cap X=\varnothing\) and \(A\cup X = B\cup X\).
Since \(A\cap X=\varnothing\), the union is a disjoint union, so \[ A = (A\cup X)\setminus X. \] Similarly, \(B = (B\cup X)\setminus X.\)
But \(A\cup X = B\cup X\). Hence \[ A = (A\cup X)\setminus X = (B\cup X)\setminus X = B. \]
Conclusion: \(\boxed{A=B}\).
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