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Relations handout

Relations handout - | = | y | • Is this relation...

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Math 100 Relations Handout Martin H. Weissman The following are relations on the set S = { a,b,c } : The ﬁrst relation is: R = { ( a,b ) , ( b,c ) , ( c,a ) , ( b,a ) , ( c,b ) , ( c,a ) } . Is this relation reﬂexive? symmetric? transitive? antisymmetric? If your answer to any of the above questions is “no”, then provide a counterexample. For example, the relation is not reﬂexive, since ( a,a ) 6∈ R . The second relation is: R = { ( a,a ) , ( a,b ) , ( a,c ) , ( b,b ) , ( b,c ) , ( c,c ) } . Is this relation reﬂexive? symmetric? transitive? antisymmetric? Provide counterexamples if your answers are “no”. Is this an equivalence relation? A partial order? The third relation is a relation on R : R = { ( x,y ) R 2 such that | x
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Unformatted text preview: | = | y |} . • Is this relation reﬂexive? symmetric? transitive? antisymmetric? • Is it an equivalence relation? a partial order? The fourth relation is a relation on S again: R = { ( a,a ) , ( a,b ) , ( b,a ) , ( b,b ) , ( c,c ) } . • Is this relation reﬂexive? symmetric? transitive? antisymmetric? • Is it an equivalence relation? a partial order? The ﬁfth relation is a relation on Z : R = { ( x,y ) ∈ Z 2 such that x-y ≥ 1 } . • Is this relation reﬂexive? symmetric? transitive? antisymmetric? • Is it an equivalence relation? a partial order? 1...
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