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We introduce Hasse diagrams for representing partially ordered sets. Recall a partially ordered set consists of a set A with a partial order R. To be a partial order, R must be transitive, antisymmetric, and reflexive. A common example is the divides relation. To create the Hasse diagram for a partially ordered set (or PO set), we represent each element in the set with a vertex, then when vertex x relates to vertex y, we draw an arrow from x to y. Then remove the arrows that exist as a result of transitivity, then redraw what remains so that all arrows are oriented in the same direction (up, down, left, or right), now the arrows can be removed as it is understood that each line indicates relation in the same direction. We'll see three examples, including a Hasse diagram for a total order. #DiscreteMath We'll also discuss minimal and maximal elements of partially ordered sets, and see how to find minimal and maximal elements in Hasse diagrams. Antisymmetric Relations: • Antisymmetric Relations | Discrete Ma... Partially Ordered Sets: • Partially Ordered Sets and Hasse Diag... Discrete Math playlist: • Discrete Math Discrete Math exercises: • Discrete Math Exercises ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Abstract Algebra: https://amzn.to/3IjoZaO Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon! Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram: / wrathofmathedu ● Facebook: / wrathofmath ● Twitter: / wrathofmathedu My Math Rap channel: / @mathbars2020