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set theory

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A) R = { (0,1),(1,0),(1,1),(1,2),(1,3),(2,1),(2,3),(3,1),(3,2),(4,1),(4,3) }.
          gcd (0,1) = 1 because 1 divides both 1 and 0 whereas gcd(0,2) = 2 because 2 divides both 0 and 2.
B) R = { (1,2),(2,1),(2,2) }.
                 There is no LCM of 0 and any non-zero integers (i.e) undefined.Because LCM(a,b)  is "the smallest positive number m for which there exist positive integers (na)(a) and (nb)(b) such that (na)(a)=(nb)(b)=m".

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R={(1,2),(2,1)} -- this is for satisfying the both conditions
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