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On (A={1,2,3,4,5}), (R={(a,b):|a-b|\text{ is even}}). What is the equivalence class of (4)?समुच्चय (A={1,2,3,4,5}) पर (R={(a,b):|a-b|\text{ सम है}}) है। (4) का तुल्यता वर्ग कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ({2,4})({2,4})
Step 1: (|a-b|) being even means (a) and (b) have the same parity. Step 2: Since (4) is even, its related elements must be even. Step 3: In the given set, the even elements are (2) and (4), so the class is ({2,4}).चरण 1: (|a-b|) सम होने का अर्थ है कि (a) और (b) की सम-विषम प्रकृति समान है। चरण 2: (4) सम है, इसलिए इससे सम्बन्धित अवयव सम होंगे। चरण 3: दिए गए समुच्चय में सम अवयव (2) और (4) हैं, अतः वर्ग ({2,4}) है।
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