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# Discussion 26 chapter 5 1415 transitivity continued

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Discussion #26 Chapter 5, Sections 3.4-4.5 14/15 Transitivity (continued…) Note: xRy yRz corresponds to xR ° Rz, which is equivalent to xR×Rz = xR 2 z; thus we can define transitivity as: 2200 x 2200 y 2200 z(xR 2 z xRz) “If I can get there in two, then I can get there in one.” For transitivity: if reachable through an intermediate, then reachable directly is required. if (x,z) R 2 , then (x,z) R (x,z) R 2 (x,z) R R 2 R ( recall our def. of subset: x A x B, then A B)

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Discussion #26 Chapter 5, Sections 3.4-4.5 15/15 Transitivity (continued…) 1 0 0 3 1 0 0 2 1 1 0 1 3 2 1 1 0 0 3 1 0 0 2 1 1 0 1 3 2 1 1 0 0 3 1 0 0 2 1 0 0 1 3 2 1 0 0 0 3 1 0 0 2 0 1 0 1 3 2 1 0 0 0 3 1 0 0 2 0 1 0 1 3 2 1 0 0 0 3 0 0 0 2 1 0 0 1 3 2 1 × = × = R R R 2 R R R R 2 R 1 2 3 Not Transitive Transitive 1 2 3
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• Winter '12
• MichaelGoodrich
• Binary relation, Transitive relation, Symmetric relation

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