यदि \(A\times B=\varnothing\) और \(A=\{0\}\), तो (B) के बारे में क्या सही है?

If \(A\times B=\varnothing\) and \(A=\{0\}\), what is true about (B)?

Explanation opens after your attempt
Correct Answer

A. \(B=\varnothing\)

Step 1

Concept

Since (A) is non-empty and \(A\times B=\varnothing\), we must have \(B=\varnothing\). An empty product means at least one set is empty.

Step 2

Why this answer is correct

The correct answer is A. \(B=\varnothing\). Since (A) is non-empty and \(A\times B=\varnothing\), we must have \(B=\varnothing\). An empty product means at least one set is empty.

Step 3

Exam Tip

क्योंकि (A) रिक्त नहीं है और \(A\times B=\varnothing\), इसलिए \(B=\varnothing\)। रिक्त गुणनफल में कम से कम एक समुच्चय रिक्त होता है।

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FAQs

Mathematics Answer, Explanation and Revision Hints

यदि \(A\times B=\varnothing\) और \(A=\{0\}\), तो (B) के बारे में क्या सही है? / If \(A\times B=\varnothing\) and \(A=\{0\}\), what is true about (B)?

Correct Answer: A. \(B=\varnothing\). Explanation: क्योंकि (A) रिक्त नहीं है और \(A\times B=\varnothing\), इसलिए \(B=\varnothing\)। रिक्त गुणनफल में कम से कम एक समुच्चय रिक्त होता है। / Since (A) is non-empty and \(A\times B=\varnothing\), we must have \(B=\varnothing\). An empty product means at least one set is empty.

Which concept should I revise for this Mathematics MCQ?

Since (A) is non-empty and \(A\times B=\varnothing\), we must have \(B=\varnothing\). An empty product means at least one set is empty.

What exam hint can help solve this Mathematics question?

क्योंकि (A) रिक्त नहीं है और \(A\times B=\varnothing\), इसलिए \(B=\varnothing\)। रिक्त गुणनफल में कम से कम एक समुच्चय रिक्त होता है।