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On (A={1,2,3,4,5}), (R={(a,b):a) is less than (b) and (b-a) is even(}). What is the nature of this relation?समुच्चय (A={1,2,3,4,5}) पर (R={(a,b):a) संख्या (b) से कम है और (b-a) सम है(}) है। यह संबंध कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Transitiveसंक्रामक
Step 1: If (a<b) and (b<c), then (a<c). Step 2: If (b-a) and (c-b) are both even, then (c-a=(c-b)+(b-a)) is also even. Hence ((a,c)) is in the relation. Step 3: In relations with combined conditions, check each condition separately.चरण 1: यदि (a<b) और (b<c), तो (a<c) होगा। चरण 2: यदि (b-a) और (c-b) दोनों सम हैं, तो (c-a=(c-b)+(b-a)) भी सम होगा। इसलिए ((a,c)) संबंध में होगा। चरण 3: संयुक्त शर्तों में हर शर्त को अलग-अलग जाँचें।
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