Unformatted text preview: R op by the following: R op = { ( a, b ) : ( b, a ) ∈ R } Show that if R is transitive then R op is also transitive. Proof Let (a,b) ∈ R op and (b,c) ∈ R op . As above we need to show that (a,c) ∈ R op . Now (a,b) ∈ R op means that (b,a) ∈ R . Similarly (c,b) ∈ R . Thus since R is transitive this means that (c,a) ∈ R . But this means that (a,c) ∈ R op . So we are done. 1...
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 Fall '08
 Enderson
 Math, Following, Christopher Nolan, rs, ROP

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