CMPSC 40 Study Guide - Midterm Guide: Existential Quantification, Constructive Proof, Codomain
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Proof = a derivation that proceeds from a set of hypotheses (premises, axioms) in order to derive a conclusion, using. Lemma = a preliminary proposition useful for proving later propositions: compound propositions = propositions constructed from other proposition and logical connectives (cid:1512) (cid:1513, propositional logic involves atomic propositions and propositional variables, ,,,. T f f: the biconditional of a statement is the negation of the exclusive-or. F f t: equivalent to the converse, precedence of logical operators: Operator precedence: same as (cid:4666) (cid:4667)(cid:1512)(cid:4666) (cid:4667, given the conditional statement , converse = , contrapositive = , equivalent . Inverse = (cid:1512) (cid:1513: or ((cid:1513)) and and ((cid:1512)) operators are associative, (cid:1513)(cid:1513)=(cid:4666)(cid:1513)(cid:4667)(cid:1513)(cid:4667)=(cid:1513)(cid:4666)(cid:1513)(cid:4667, is not associative, for atomic propositions, you need (cid:884)(cid:3041) rows in a truth table, use the symbol (cid:1568) to denote equivalence. (cid:4666)(cid:1513)(cid:4667) (cid:4666)(cid:1512)(cid:4667) ((cid:4666)(cid:4667)(cid:1512)(cid:4666)(cid:4667)) (cid:4666)(cid:1512)(cid:4667) ((cid:4666) (cid:1513)(cid:4667)(cid:1512)(cid:4666)(cid:1513)(cid:4667)) (cid:4666)(cid:1513)(cid:4667: proof = a valid argument that establishes the truth of a statement, for conditional statement :
