Class 12 Mathematics - Relations and Functions - Onto function Expert Quiz

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यदि \(R=\{(a,b):\min(a,b)=a\}\) वास्तविक संख्याओं पर है, तो (R) के बारे में सही कथन क्या है?

If \(R=\{(a,b):\min(a,b)=a\}\) is defined on real numbers, what is true about (R)?

Explanation opens after your attempt
Correct Answer

A. सममित नहीं हैIt is not symmetric

Step 1

Concept

(\min(a,b)=a) means \(a\le b\).

Step 2

Why this answer is correct

((1,2)) is in the relation, but ((2,1)) is not.

Step 3

Exam Tip

In such questions, first convert the condition into a familiar inequality. चरण 1: (\min(a,b)=a) का अर्थ है \(a\le b\)। चरण 2: ((1,2)) संबंध में है, लेकिन ((2,1)) संबंध में नहीं है। चरण 3: छिपी हुई असमानता पहचानना ऐसे प्रश्नों में जरूरी है।

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यदि \(R=\{(a,b):\max(a,b)=\max(b,a)\}\) वास्तविक संख्याओं पर है, तो (R) के बारे में सही कथन क्या है?

If \(R=\{(a,b):\max(a,b)=\max(b,a)\}\) is defined on real numbers, what is true about (R)?

Explanation opens after your attempt
Correct Answer

A. यह सार्वत्रिक और सममित हैIt is universal and symmetric

Step 1

Concept

(\max(a,b)=\max(b,a)) is true for all real (a,b).

Step 2

Why this answer is correct

So the relation contains every ordered pair, making it universal.

Step 3

Exam Tip

A universal relation is always symmetric because every reverse pair is present. चरण 1: (\max(a,b)=\max(b,a)) हर वास्तविक (a,b) के लिए सत्य है। चरण 2: इसलिए संबंध सभी युग्मों को रखता है, यानी यह सार्वत्रिक संबंध है। चरण 3: सार्वत्रिक संबंध हमेशा सममित होता है क्योंकि सभी उल्टे युग्म भी मौजूद होते हैं।

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