Class 12 Mathematics - Relations and Functions - Functions Medium Quiz

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संबंध (R) को \(A=\{1,2,3\}\) पर (aRb) तभी जब (a=b) से परिभाषित किया गया है। (R) कैसा है?

A relation (R) on \(A=\{1,2,3\}\) is defined by (aRb) if and only if (a=b). What type is (R)?

Explanation opens after your attempt
Correct Answer

B. तत्समक संबंधIdentity relation

Step 1

Concept

The condition (a=b) gives only self-pairs.

Step 2

Why this answer is correct

So the relation is limited to ((1,1),(2,2),(3,3)).

Step 3

Exam Tip

Whenever you see (a=b), identify the identity relation. चरण 1: शर्त (a=b) केवल अपने-अपने युग्म बनाती है। चरण 2: इसलिए संबंध ((1,1),(2,2),(3,3)) तक सीमित है। चरण 3: (a=b) दिखते ही तत्समक संबंध पहचानें।

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समुच्चय \(A=\{1,2,3\}\) पर कौन-सा संबंध संक्रमणीय है?

Which relation on \(A=\{1,2,3\}\) is transitive?

Explanation opens after your attempt
Correct Answer

B. ({(1,2),(2,3),(1,3)})

Step 1

Concept

((1,2)) and ((2,3)) require ((1,3)).

Step 2

Why this answer is correct

The second option contains this required pair.

Step 3

Exam Tip

In transitivity, check only pairs that can be linked through a middle element. चरण 1: ((1,2)) और ((2,3)) से ((1,3)) चाहिए। चरण 2: दूसरे विकल्प में यह जरूरी युग्म मौजूद है। चरण 3: संक्रमणीयता में केवल जुड़े हुए युग्मों से बनने वाले युग्मों को जाँचें।

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