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Relasi transitif - Riwayat revisi
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Sumber dan atribusi ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Sumber dan atribusi ==</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Relasi+transitif&oldid=22502776 Wikipedia bahasa Indonesia], revisi 22502776 (2022-12-28T10:50:55Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Mohon gunakan konten ini secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Relasi+transitif&oldid=22502776 Wikipedia bahasa Indonesia], revisi 22502776 (2022-12-28T10:50:55Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Mohon gunakan konten ini secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.</div></td></tr>
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Maintenance script: Impor teks terkontrol dari Wikipedia bahasa Indonesia; revisi 22502776; atribusi sumber disertakan.
2026-08-27T03:53:19Z
<p>Impor teks terkontrol dari Wikipedia bahasa Indonesia; revisi 22502776; atribusi sumber disertakan.</p>
<p><b>Halaman baru</b></p><div>Dalam matematika, [[Relasi (matematika)|relasi]] <math>R</math> pada himpunan <math>X</math> dikatakan '''transitif''' jika <math>R</math> menghubungkan <math>a</math> ke <math>b</math> dan menghubungkan <math>b</math> ke <math>c</math>, maka <math>R</math> menghubungkan <math>a</math> ke <math>c</math>.<br />
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== Definisi ==<br />
[[Relasi homogen]] <math>R</math> pada himpunan <math>X</math> dikatakan ''transitif'' jika <math>aRb</math> dan <math>bRc</math>, maka <math>aRc</math>, untuk semua <math>a,b,c, \in X</math>. Secara matematis, dapat ditulis dalam notasi [[Logika predikat tingkat pertama|logika orde pertama]].<br />
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<math display="block">\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc.</math><br />
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Pada notasi di atas, <math>aRb</math> merupakan [[notasi infiks]] untuk <math>(a,b) \in R</math>.<br />
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== Contoh ==<br />
Contoh relasi transitif dalam matematika memuat "lebih besar dari" dan "[[Kesamaan (matematika)|sama dengan]]"; dalam himpunan [[bilangan real]] atau [[bilangan asli]].<br />
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* jika <math>x>y</math>, dan <math>y>z</math>, maka <math>x>z</math><br />
* jika <math>x=y</math>, dan <math>y=z</math>, maka <math>x=z</math>.<br />
Relasi transitif dapat dinyatakan juga melalui contoh-contoh non-matematis, seperti relasi "leluhur dari"; sebagai contoh, jika Ani adalah leluhur dari Budi, dan Budi adalah leluhur dari Candra, maka Ani adalah leluhur dari Candra.<br />
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== Catatan ==<br />
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== Referensi ==<br />
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== Sumber dan atribusi ==<br />
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Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Relasi+transitif&oldid=22502776 Wikipedia bahasa Indonesia], revisi 22502776 (2022-12-28T10:50:55Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Mohon gunakan konten ini secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.</div>
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