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1: Propositional Logic

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The grand aim of all science is to cover the greatest number of empirical facts
by logical deduction from the smallest number of hypotheses or axioms.

Albert Einstein (1879–1955), Nobel prize-winning physicis
in Life magazine

For our purposes, Logic is the business of deciding whether or not a deduction is valid; that is, deciding whether or not a particular conclusion is a consequence of particular assumptions. (The assumptions can also be called “hypotheses” or “axioms.”)