यदि \(U=\{1,2,3,4,5,6\}\) है और (A) ऐसा समुच्चय है कि \(A=A^c\), तो कौन सा कथन सही है?
If \(U=\{1,2,3,4,5,6\}\) and (A) is a set such that \(A=A^c\), which statement is correct?
Explanation opens after your attempt
Correct Answer
A. ऐसा कोई (A) नहीं हो सकताno such (A) can exist
Concept
If \(A=A^c\), then \(A\cap A^c=A\), but \(A\cap A^c=\varnothing\). This would force \(A=\varnothing\), but then \(A^c=U\), so it is impossible.
Why this answer is correct
The correct answer is A. ऐसा कोई (A) नहीं हो सकता / no such (A) can exist. If \(A=A^c\), then \(A\cap A^c=A\), but \(A\cap A^c=\varnothing\). This would force \(A=\varnothing\), but then \(A^c=U\), so it is impossible.
Exam Tip
यदि \(A=A^c\), तो \(A\cap A^c=A\) होगा, लेकिन \(A\cap A^c=\varnothing\) होता है। इससे \(A=\varnothing\) चाहिए, पर तब \(A^c=U\), इसलिए संभव नहीं है।
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