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On (A={1,2,3,4}), (R={(a,b):a-b\equiv 0 \pmod{3}}). What can be said about (R)?समुच्चय (A={1,2,3,4}) पर (R={(a,b):a-b\equiv 0 \pmod{3}}) है। (R) कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is symmetricसममित है
Step 1: (a-b\equiv 0 \pmod{3}) means (a) and (b) have the same remainder modulo (3). Step 2: Then (b-a\equiv 0 \pmod{3}) also holds. Step 3: Congruence equality conditions remain valid after reversing the pair.चरण 1: (a-b\equiv 0 \pmod{3}) का अर्थ है कि (a) और (b) समान अवशेष देते हैं। चरण 2: तब (b-a\equiv 0 \pmod{3}) भी होगा। चरण 3: मापांक में समानता वाली शर्तें उलटने पर भी बनी रहती हैं।
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