Class 12 Mathematics - Relations and Functions - Functions Hard Quiz

Mathematics Relations and Functions Functions Hard Class 12 Level 15

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Question 1/1 Hard Mathematics Relations and Functions Transitive relation Class 12 Level 15

समुच्चय \(A=\{1,2,3,4\}\) पर संबंध \(R=\{(a,b):a\le b\}\) दिया है। यह संबंध संक्रमणीय क्यों है?

On the set \(A=\{1,2,3,4\}\), the relation \(R=\{(a,b):a\le b\}\) is given. Why is this relation transitive?

Explanation opens after your attempt
Correct Answer

A. क्योंकि \(a\le b\) और \(b\le c\) से \(a\le c\) मिलता हैBecause \(a\le b\) and \(b\le c\) imply \(a\le c\)

Step 1

Concept

For transitivity, if \((a,b)\in R\) and \((b,c)\in R\), then \((a,c)\in R\) must hold.

Step 2

Why this answer is correct

Here \(a\le b\) and \(b\le c\) directly imply \(a\le c\).

Step 3

Exam Tip

In exams, check inequality relations by forming a chain. चरण 1: संक्रमणीयता में यदि \((a,b)\in R\) और \((b,c)\in R\) हों तो \((a,c)\in R\) होना चाहिए। चरण 2: यहां \(a\le b\) और \(b\le c\) से सीधे \(a\le c\) मिलता है। चरण 3: परीक्षा में असमानता वाले संबंधों में पहले क्रम की श्रृंखला बनाकर जांचें।

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