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During the course work of the Biological and Cognitive Sciences, we study many important concept of the cognitive sciences, the key points are:Patterns, Presume, Corrolaries, Deduction, Contradiction, Induction, Deriving, Contradiction, Incremental Steps, Demonstratum
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All theorems, lemmas, corrolaries presume something and then prove something else. Deduction: utilize logical rules of inference. Contradiction: prove that something is not true by deriving a contradiction from assuming it. Induction: prove a large result in incremental steps. Several useful patterns: Proof Patterns Docsity.com
Q.E.D. = Quod Erat Demonstratum = "that which was to be demonstrated." This ends every proof. Reductio Ad Absurdum = "reduction to a contradiction" Two Latin phrases used in proofs: Some Latin Magic Docsity.com
Universal instantiation: from general to specific. Universal generalization: from specific to general. Existential instantiation: from quantifier to instance. Existential generalization: from instance to quantifier. instantiation: process of setting a variable to a value. Rules for quantifiers Docsity.com
Universal instantiation Docsity.com
Existential instantiation Docsity.com
Existential generalization Docsity.com
The idea of contradiction: if we can use our suppositions to prove both p and not p, then our suppositions are inconsistent! Proof by contradiction Docsity.com
