Unformatted text preview: productdigits, consider the following relation: {(a,b)  a âˆˆ Z + âˆ§ b âˆˆ Z + âˆ§ (a â‰¥ b âˆ¨ productdigits(a) â‰¥ productdigits(b)} Determine if this relation is (i)reflexive, (ii)irreflexive, (iii)symmetric, (iv)antisymmetric, and (v)transitive? 6) Prove that following function is a bijection from the open interval (0,3) to the positive real numbers: x x x f 3 3 ) (= For the last few questions assume that R and T are arbitrary binary relations over ZxZ. Disprove each of the following assertions: (Note: r, s, and t represent the reflexive, symmetric and transitive closures of relations.) 7) If s( R) is transitive, then R is transitive. 8) If R is transitive and R âŠ† T , then T is transitive. 9) For all relations R , t(s( R )) is reflexive. 10) For all relations R, t(s( R )) = s(t( R ))....
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 Spring '09
 Equivalence relation, Binary relation, Transitive relation

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