Answer to Question #279195 in Discrete Mathematics for Jai

Question #279195

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.

1
Expert's answer
2021-12-14T17:35:35-0500

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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