Solution to If A = {1, 2, 3, 4, 6, 12} then define a relation R by … - Sikademy
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Archangel Macsika

If A = {1, 2, 3, 4, 6, 12} then define a relation R by aRb if and only if a divides b. Prove that R is a partial order on A.

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A binary relation is a partial order if and only if the relation is reflexive, antisymmetric and transitive

R=\{(1,1),(1,2),(1,3),(1,4),(1,6),(1,12),(2,2),(2,4),(2,6),(2,12),(3,6),

(3,12),(4,12),(6,12),(3,3),(4,4),(6,6),(12,12)\}


R is reflexive: (1,1),(2,2)(3,3),(4,4),(6,6),(12,12)\isin R

R is antisymmetric: if (a,b)\isin R then (b,a)\notin R for a\neq b

R is transitive: if aRb and bRc then aRc for all a,b,c\isin A

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