Class 11 Mathematics Relations and Functions Relations Expert Level 27

समुच्चय \(A=\{1,2,3,4,5,6\}\) पर (aRb) तभी जब (a) और (b) का समान greatest prime factor हो। यह relation कैसी है?

On \(A=\{1,2,3,4,5,6\}\), (aRb) if and only if (a) and (b) have the same greatest prime factor. What kind of relation is it?

Explanation opens after your attempt
Correct Answer

A. तुल्यता संबंधEquivalence relation

Step 1

Concept

Having the same greatest prime factor behaves like equality, so it is reflexive, symmetric, and transitive. Such same invariant conditions often give equivalence relations.

Step 2

Why this answer is correct

The correct answer is A. तुल्यता संबंध / Equivalence relation. Having the same greatest prime factor behaves like equality, so it is reflexive, symmetric, and transitive. Such same invariant conditions often give equivalence relations.

Step 3

Exam Tip

एक ही greatest prime factor होना equality जैसी condition है, इसलिए reflexive, symmetric और transitive है। ऐसी same invariant वाली conditions अक्सर equivalence relation देती हैं।

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Mathematics Answer, Explanation and Revision Hints

समुच्चय \(A=\{1,2,3,4,5,6\}\) पर (aRb) तभी जब (a) और (b) का समान greatest prime factor हो। यह relation कैसी है? / On \(A=\{1,2,3,4,5,6\}\), (aRb) if and only if (a) and (b) have the same greatest prime factor. What kind of relation is it?

Correct Answer: A. तुल्यता संबंध / Equivalence relation. Explanation: एक ही greatest prime factor होना equality जैसी condition है, इसलिए reflexive, symmetric और transitive है। ऐसी same invariant वाली conditions अक्सर equivalence relation देती हैं। / Having the same greatest prime factor behaves like equality, so it is reflexive, symmetric, and transitive. Such same invariant conditions often give equivalence relations.

Which concept should I revise for this Mathematics MCQ?

Having the same greatest prime factor behaves like equality, so it is reflexive, symmetric, and transitive. Such same invariant conditions often give equivalence relations.

What exam hint can help solve this Mathematics question?

एक ही greatest prime factor होना equality जैसी condition है, इसलिए reflexive, symmetric और transitive है। ऐसी same invariant वाली conditions अक्सर equivalence relation देती हैं।