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If (R) is an equivalence relation on a set (A) and ([a]\subseteq[b]), what conclusion is definite?यदि (R) किसी समुच्चय (A) पर तुल्यता सम्बन्ध है और ([a]\subseteq[b]), तो क्या निष्कर्ष निश्चित है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ([a]=[b])([a]=[b])
Step 1: (a) always belongs to its own class ([a]). Step 2: Since ([a]\subseteq[b]), we get (a\in[b]), so (a) and (b) are related. Step 3: In an equivalence relation, related elements have equal classes, hence ([a]=[b]).चरण 1: (a) हमेशा अपने वर्ग ([a]) में होता है। चरण 2: ([a]\subseteq[b]) होने से (a\in[b]), इसलिए (a) और (b) सम्बन्धित हैं। चरण 3: तुल्यता सम्बन्ध में सम्बन्धित अवयवों के वर्ग समान होते हैं, अतः ([a]=[b])।
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