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logica cuantificacional
- 1. 3.1 𝐿𝑎𝑠 𝑒𝑚𝑝𝑟𝑒𝑠𝑎𝑠 𝑠𝑜𝑙𝑖𝑐𝑖𝑡𝑎𝑛 𝑝𝑟𝑎𝑐𝑡𝑖𝑐𝑎𝑛𝑡𝑒𝑠⏟ 𝑃𝑥 , 𝑝𝑒𝑟𝑜⏟ ∧ 𝑛𝑜 𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑎𝑛 𝑞𝑢𝑒 𝑠𝑒𝑎𝑛 𝑒𝑔𝑟𝑒𝑠𝑎𝑑𝑜𝑠⏟ −𝐸 𝑥 ; 𝑎𝑙 𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑎𝑟 𝑞𝑢𝑒 𝑠𝑒𝑎𝑛 𝑒𝑔𝑟𝑒𝑠𝑎𝑑𝑜𝑠⏟ 𝐸 𝑥 𝑜⏟ ∨ 𝑛𝑜 ℎ𝑎𝑦𝑎𝑛 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑑𝑜 𝑠𝑢𝑠 𝑒𝑠𝑡𝑢𝑑𝑖𝑜𝑠 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑎𝑟𝑖𝑜𝑠⏟ −𝑈 𝑥 , 𝑠𝑖 𝑒𝑠𝑡á𝑛 𝑡𝑟𝑎𝑏𝑎𝑗𝑎𝑛𝑑𝑜 𝑒𝑛 𝑙𝑎𝑠 𝑒𝑚𝑝𝑟𝑒𝑠𝑎𝑠⏟ 𝑇𝑥 𝑒𝑛𝑡𝑜𝑛𝑐𝑒𝑠⏟ ⟶ ℎ𝑎𝑛 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑑𝑜 𝑠𝑢𝑠 𝑒𝑠𝑡𝑢𝑑𝑖𝑜𝑠 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑎𝑟𝑖𝑜𝑠⏟ 𝑈 𝑥 , pero si 𝑛𝑜 𝑒𝑠𝑡á𝑛 𝑡𝑟𝑎𝑏𝑎𝑗𝑎𝑛𝑑𝑜 𝑒𝑛 𝑙𝑎𝑠 𝑒𝑚𝑝𝑟𝑒𝑠𝑎𝑠⏟ 𝑇𝑥 𝑖𝑚𝑝𝑙𝑖𝑐𝑎𝑛 𝑞𝑢𝑒⏟ ⟶ 𝑒𝑠𝑡á𝑛 𝑑𝑖𝑠𝑝𝑜𝑛𝑖𝑏𝑙𝑒𝑠⏟ 𝐷 𝑥 . Por lo tanto, 𝑒𝑠𝑡á𝑛 𝑑𝑖𝑠𝑝𝑜𝑛𝑖𝑏𝑙𝑒𝑠⏟ 𝐷 𝑥 𝑦⏟ ∧ 𝑙𝑎𝑠 𝑒𝑚𝑝𝑟𝑒𝑠𝑎𝑠 𝑠𝑜𝑙𝑖𝑐𝑖𝑡𝑎𝑛 𝑝𝑟𝑎𝑐𝑡𝑖𝑐𝑎𝑛𝑡𝑒𝑠⏟ 𝑃𝑥 3.2 𝑆𝑖 𝑙𝑜𝑠 𝑒𝑠𝑡𝑢𝑑𝑖𝑎𝑛𝑡𝑒𝑠 𝑜𝑏𝑡𝑖𝑒𝑛𝑒𝑛 𝑒𝑙 𝑝𝑟𝑖𝑚𝑒𝑟 𝑝𝑢𝑒𝑠𝑡𝑜⏟ 𝑃 𝑥 , 𝑒𝑛𝑡𝑜𝑛𝑐𝑒𝑠⏟ ⟶ 𝑔𝑎𝑛𝑎𝑟𝑜𝑛 𝑡𝑜𝑑𝑎𝑠 𝑙𝑎𝑠 𝑐𝑜𝑚𝑝𝑒𝑡𝑒𝑛𝑐𝑖𝑎𝑠⏟ 𝐺 𝑥 ; 𝑜𝑏𝑡𝑖𝑒𝑛𝑒𝑛 𝑒𝑙 𝑝𝑟𝑖𝑚𝑒𝑟 𝑝𝑢𝑒𝑠𝑡𝑜⏟ 𝑃 𝑥 𝑜⏟ ∨ ℎ𝑖𝑐𝑖𝑒𝑟𝑜𝑛 𝑙𝑎𝑠 𝑡𝑎𝑟𝑒𝑎𝑠 𝑑𝑒𝑗𝑎𝑑𝑎𝑠 𝑝𝑜𝑟 𝑙𝑜𝑠 𝑑𝑜𝑐𝑒𝑛𝑡𝑒𝑠⏟ 𝑇𝑥 ; 𝑠𝑖 ℎ𝑎𝑐𝑒𝑛 𝑙𝑎𝑠 𝑡𝑎𝑟𝑒𝑎𝑠 𝑑𝑒𝑗𝑎𝑑𝑎𝑠 𝑝𝑜𝑟 𝑙𝑜𝑠 𝑑𝑜𝑐𝑒𝑛𝑡𝑒𝑠⏟ 𝑇𝑥 𝑒𝑛𝑡𝑜𝑛𝑐𝑒𝑠⏟ ⟶ 𝑎𝑠𝑖𝑠𝑡𝑖𝑒𝑟𝑜𝑛 𝑎 𝑐𝑙𝑎𝑠𝑒𝑠⏟ 𝐶 𝑥 ; 𝑠𝑖 𝑔𝑎𝑛𝑎𝑟𝑜𝑛 𝑡𝑜𝑑𝑎𝑠 𝑙𝑎𝑠 𝑐𝑜𝑚𝑝𝑒𝑡𝑒𝑛𝑐𝑖𝑎𝑠⏟ 𝐺 𝑥 𝑒𝑛𝑡𝑜𝑛𝑐𝑒𝑠⏟ ⟶ 𝑝𝑎𝑟𝑡𝑖𝑐𝑖𝑝𝑎𝑟𝑜𝑛 𝑡𝑜𝑑𝑜 𝑒𝑙 𝑠𝑎𝑙ó𝑛⏟ 𝑆 𝑥 por lo tanto, 𝑠𝑖 𝑛𝑜 𝑎𝑠𝑖𝑠𝑡𝑒𝑛 𝑎 𝑐𝑙𝑎𝑠𝑒𝑠⏟ −𝐶 𝑥 𝑖𝑚𝑝𝑙𝑖𝑐𝑎⏟ ⟶ que 𝑝𝑎𝑟𝑡𝑖𝑐𝑖𝑝𝑜 𝑡𝑜𝑑𝑜 𝑒𝑙 𝑠𝑎𝑙ó𝑛⏟ 𝑆 𝑥 3.1