Day 03Part 11-Discrete Mathematics-Example on lattice How to find a hasse diagram is lattice or not<\/p>\n
[fvplayer id=”220″]<\/p>\n
A Hasse diagram<\/strong> is a graphical representation of a partially ordered set (poset)<\/strong>. It helps in visualizing relationships between elements.<\/p>\n Rules for drawing a Hasse diagram:<\/strong><\/p>\n A poset is a Lattice<\/strong> if every pair of elements has<\/strong>:<\/p>\n Steps to Check:<\/strong> Consider the set S = {1, 2, 3, 6}<\/strong> under divisibility. Check Join (\u2228) and Meet (\u2227):<\/strong><\/p>\n Join (\u2228):<\/strong><\/p>\n Meet (\u2227):<\/strong><\/p>\n Conclusion:<\/strong> Every pair has a Join & Meet \u2192 It is a Lattice!<\/strong><\/p>\n Consider the set {a, b, c, d}<\/strong> with the following Hasse diagram:<\/p>\n Check Join (\u2228) and Meet (\u2227):<\/strong><\/p>\n \u00a0Since b and c<\/strong> do not have a unique LUB (Join)<\/strong>, this is NOT a Lattice!<\/strong><\/p>\n A poset is a Lattice if every two elements have a Join (\u2228) and a Meet (\u2227).<\/strong> Would you like more examples or step-by-step solved problems<\/strong>?<\/p>\n \u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938<\/strong> \u092e\u0947\u0902 \u0932\u0948\u091f\u093f\u0938 (Lattice)<\/strong> \u090f\u0915 \u0935\u093f\u0936\u0947\u0937 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u093e \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f (Poset)<\/strong> \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092f\u0941\u0917\u094d\u092e (pair) \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0905\u0926\u094d\u0935\u093f\u0924\u0940\u092f Least Upper Bound (LUB)<\/strong> \u0914\u0930 Greatest Lower Bound (GLB)<\/strong> \u0939\u094b\u0924\u093e \u0939\u0948\u0964 Hasse Diagram<\/strong> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092f\u0939 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u094b\u0908 Poset \u0932\u0948\u091f\u093f\u0938 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902\u0964<\/p>\n Hasse Diagram \u090f\u0915 \u0917\u094d\u0930\u093e\u092b\u093f\u0915\u0932 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0939\u0948 \u091c\u094b Poset \u0915\u0947 \u0924\u0924\u094d\u0935\u094b\u0902 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u092e\u0947\u0902 \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0906\u0926\u0947\u0936 \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0915\u094b \u0930\u0947\u0916\u093e\u0913\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 Hasse Diagram \u0915\u0940 \u0938\u0939\u093e\u092f\u0924\u093e \u0938\u0947 \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091a\u0930\u0923\u094b\u0902 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0915\u0947 \u092f\u0939 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u094b\u0908 Poset \u0932\u0948\u091f\u093f\u0938 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902:<\/p>\n \u0928\u0940\u091a\u0947 \u0926\u093f\u090f \u0917\u090f \u0935\u0940\u0921\u093f\u092f\u094b \u092e\u0947\u0902 Hasse Diagram \u0915\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092f\u0939 \u0938\u092e\u091d\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u093f \u0915\u0948\u0938\u0947 \u092f\u0939 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u090f \u0915\u093f \u0915\u094b\u0908 Poset \u0932\u0948\u091f\u093f\u0938 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902:<\/p>\n CHECK WHETHER 15 HASSE DIAGRAMS ARE LATTICES OR …<\/p>\n \u092f\u0926\u093f \u0906\u092a \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 Hasse Diagram \u092f\u093e Poset \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923 \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u0943\u092a\u092f\u093e \u0935\u093f\u0935\u0930\u0923 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0947\u0902, \u0924\u093e\u0915\u093f \u0939\u092e \u0909\u0938 \u092a\u0930 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0938\u0947 \u091a\u0930\u094d\u091a\u093e \u0915\u0930 \u0938\u0915\u0947\u0902\u0964<\/p>\n Day 03Part 11-Discrete Mathematics-Example on lattice How to find a hasse diagram is lattice or not [fvplayer id=”220″] \u00a0Day 03 | Part 11 \u2013 Discrete Mathematics \u00a0Example on Lattice: How to Check if a Hasse Diagram is a Lattice? \u00a0What is a Hasse Diagram? A Hasse diagram is a graphical representation of a partially ordered […]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[76],"tags":[],"class_list":["post-3021","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3021","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=3021"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3021\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\u00a0How to Check if a Hasse Diagram is a Lattice?<\/strong><\/h3>\n
\n
Draw the Hasse Diagram<\/strong> of the given poset.
Pick any two elements<\/strong> and find their:<\/p>\n\n
Check for all pairs<\/strong> \u2013 If every pair has both Join & Meet, it is a Lattice<\/strong>.<\/li>\n<\/ul>\n\u00a0Example: Check if the Following Poset Forms a Lattice<\/strong><\/h3>\n
The Hasse diagram is:<\/p>\n 6
\n\/ \\
\n2 3
\n\\ \/
\n1
\n<\/span><\/code><\/div>\n<\/div>\n\n
\n
\n
\u00a0Example: A Poset That is NOT a Lattice<\/strong><\/h3>\n
a<\/span>
\n\/ \\
\nb<\/span> c
\n\\ \/
\nd
\n<\/code><\/div>\n<\/div>\n\n
\u00a0Key Takeaways<\/strong><\/h3>\n
Use Hasse diagrams to check Join & Meet for all pairs.<\/strong>
If any pair lacks Join or Meet, the poset is NOT a Lattice.<\/strong><\/p>\nDay 03Part 11-Discrete Mathematics-Example on lattice How to find a hasse diagram is lattice or not<\/a><\/h3>\n
\n\ud83d\udd0d Hasse Diagram \u0938\u0947 \u0932\u0948\u091f\u093f\u0938 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902?<\/h2>\n
\n
\n
\n
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\n\ud83d\udcca Hasse Diagram \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923<\/h2>\n
\nDay 03Part 11-Discrete Mathematics-Example on lattice How to find a hasse diagram is lattice or not<\/a><\/h3>\n
Hasse Diagram\u00a0<\/a><\/h3>\n
Notes on Lattice Theory<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"