{"id":27416,"date":"2021-01-28T13:00:29","date_gmt":"2021-01-28T13:00:29","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27416"},"modified":"2024-07-09T02:18:52","modified_gmt":"2024-07-09T02:18:52","slug":"5-symmetries-of-propositional-logic","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/en\/5-symmetries-of-propositional-logic\/","title":{"rendered":"5 Symmetries of Propositional Logic"},"content":{"rendered":"
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5 Symmetries of Propositional Logic<\/h1>\n

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Summary:<\/strong>
Throughout this class, we will explore how double negation, hypothetical syllogism, the contrapositive of implication, deduction theorems, and the definitions of connectors combine to form the symmetries of propositional logic. With clear and simple demonstrations, you will learn to master the equivalences and apply them to your own logical challenges.<\/p>\n

The symmetries addressed in the class include: \\downarrow<\/span>-Symmetry, \\vee<\/span>-Symmetry, \\wedge<\/span>-Symmetry, \\leftrightarrow<\/span>-Symmetry, and \\veebar<\/span>-Symmetry. Additionally, the interactions between the demonstrations are highlighted, showing how each one supports the previous ones to simplify future deductions. This class will not only provide you with a deep understanding of Propositional Logic but also teach you to use previous demonstrations to optimize your learning process.
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Learning Objectives<\/u>:<\/strong>
By the end of this class, the student will be able to<\/p>\n

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  1. Recall<\/strong> basic concepts of propositional logic, such as hypothetical syllogism and double negation.<\/li>\n
  2. Recognize<\/strong> the 5 Symmetries of Propositional Logic.<\/li>\n
  3. Understand<\/strong> the process of demonstrating symmetry equivalences.<\/li>\n
  4. Apply<\/strong> Presumption, Deduction Theorem, and its Reciprocal in demonstrations.<\/li>\n
  5. Relate<\/strong> the definitions of logical connectors to the symmetries.<\/li>\n
  6. Appreciate<\/strong> the importance of performing demonstrations only once and reusing them in future demonstrations.<\/li>\n
  7. Develop<\/strong> analytical and critical skills when performing logical demonstrations.<\/li>\n<\/ol>\n

    CONTENTS INDEX<\/strong>
    \n\\vee<\/span> – SYMMETRY<\/a>
    \n    \\downarrow<\/span> – SYMMETRY<\/a>
    \n    \\wedge<\/span> – SYMMETRY<\/a>
    \n    \\leftrightarrow<\/span> – SYMMETRY<\/a>
    \n    \\veebar<\/span> – SYMMETRY<\/a>
    \n    FINAL REMARKS<\/a>\n<\/p>\n


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