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On integers, (aRb) if (a \equiv b \pmod{3}). Is (R) transitive?पूर्णांकों पर (aRb) तब है जब (a \equiv b \pmod{3})। क्या (R) संक्रामी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Yesहाँ
Step 1: If (a \equiv b \pmod{3}) and (b \equiv c \pmod{3}), then (a) and (c) have the same remainder. Step 2: So (a \equiv c \pmod{3}). Step 3: A relation based on the same remainder is transitive.चरण 1: यदि (a \equiv b \pmod{3}) और (b \equiv c \pmod{3}), तो (a) और (c) का शेष समान होगा। चरण 2: इसलिए (a \equiv c \pmod{3}) होगा। चरण 3: समान शेष वाला संबंध संक्रामी होता है।
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