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Estructuras Discretas 2 - Algebras Booleanas
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Miguel yustiz
1.
𝐷𝑒𝑚𝑜𝑠𝑡𝑟𝑎𝑟 𝑠𝑖 𝑙𝑜𝑠
𝑠𝑖𝑔𝑢𝑖𝑒𝑛𝑡𝑒𝑠 𝑝𝑜𝑙𝑖𝑛𝑜𝑚𝑖𝑜𝑠 𝑠𝑜𝑛 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡𝑒𝑠: 𝑃 (𝑤, 𝑥, 𝑦, 𝑧) = 𝑤𝑥 + (𝑥’’ + 𝑧’) + (𝑦 + 𝑧’) 𝑄 (𝑤, 𝑥, 𝑦, 𝑧) = 𝑥 + 𝑧’ + 𝑦 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑖𝑐𝑜 𝑃 (𝑤, 𝑥, 𝑦, 𝑧) 𝑃 (𝑤, 𝑥, 𝑦, 𝑧) = 𝑤𝑥 + (𝑥’’ + 𝑧’) + (𝑦 + 𝑧’’) 𝑃 (𝑤, 𝑥, 𝑦, 𝑧) = 𝑤𝑥 + (𝑥 + 𝑧’) + (𝑦 + 𝑧’’) −>> 𝑥’’ = 𝑥 = (𝑤𝑥 + 𝑥) + (𝑧’ + 𝑧’) + 𝑦 −>> 𝑙𝑒𝑦 𝑎𝑠𝑜𝑐𝑖𝑎𝑡𝑖𝑣𝑎 = 𝑥 + (𝑧’ + 𝑧’) + 𝑦 −>> 𝑙𝑒𝑦 𝑎𝑠𝑜𝑐𝑖𝑎𝑡𝑖𝑣𝑎 𝑃 (𝑤, 𝑥, 𝑦, 𝑧) = 𝑥 + 𝑧’ + 𝑦 𝑃𝑜𝑟 𝑙𝑜 𝑡𝑎𝑛𝑡𝑜 𝑃 (𝑤, 𝑥, 𝑦, 𝑧) = 𝑄 (𝑤, 𝑥, 𝑦, 𝑧) 𝑷 𝒚 𝑸 𝒔𝒐𝒏 𝒆𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕𝒆𝒔. 𝑃 (𝑤, 𝑥, 𝑦, 𝑧) = 𝑤𝑥 + (𝑥’’ + 𝑧’) ́ + (𝑦𝑧’) ́ 𝑤 ́ 𝑪𝒊𝒓𝒄𝒖𝒊𝒕𝒐 𝑳ó𝒈𝒊𝒄𝒐
2.
𝑻𝒂𝒃𝒍𝒂 𝒅𝒆 𝒍𝒂
𝒗𝒆𝒓𝒅𝒂𝒅. 𝑋 𝑌 𝑍 𝑊 𝑊𝑋 𝑋’’ 𝑍’ 𝑊’ (𝑋’’ + 𝑍’)’ (𝑌𝑍’)𝑊’ 𝑃(𝑊, 𝑋, 𝑌, 𝑍) 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0
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