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In Classical Deductive reasoning, you cannot say anything about Q -> P from P -> Q. However, probabilistic reasoning allows you to say something about the probability of Q given P from the probability of P given Q. The attached document explores this through two examples.
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Providing students with the ability to justify claims is one of the basic commitments of Inquiry Oriented Education. The attached documents explores the concepts involved in justification as well as bunch of exercises and examples for students to engage with.
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Mathematics is the study of possible worlds. The attached document explores, through examples and exposition, the nature of mathematical inquiry as well as the concepts involved in the study of mathematics, namely axioms, definitions, conjectures, proofs and theorems.
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