Engineering Mathematics · topic
Propositional laws, normal forms, tautology and satisfiability, valid arguments and inference rules, functional completeness; first-order logic with quantifier negation, nested quantifier order, distribution laws and translation of English statements.
Connectives and their truth conditions, the equivalence laws (De Morgan, distributive, absorption, implication, contrapositive, biconditional, exportation), how implications split over conjunction and disjunction, converse, inverse and contrapositive, disjunctive and conjunctive normal forms with minterms and maxterms, a conversion routine to CNF, and counts of Boolean functions. Every law is checked by a full truth table in the verification script.
A partial preview of the top of the sheet. The full sheet is in the Engineering Mathematics cheat sheet pack.
Tautology, contradiction, contingency and satisfiability and how they relate, logical consequence, testing an argument by looking only at rows where the conclusion is false, the standard inference rules, the two classic fallacies, resolution refutation, translating English conditionals (only if, unless, necessary, sufficient), and functional completeness with Post's five classes and NAND constructions. All claims are checked by truth tables or closure computations.
A partial preview of the top of the sheet. The full sheet is in the Engineering Mathematics cheat sheet pack.
Predicates, domains, free and bound variables, quantifier negation, which distribution laws hold both ways and which hold one way, moving a quantifier past a formula that does not mention its variable (including the implication traps), the order of nested quantifiers, translating all, some, no, only and exactly one, inference rules for quantifiers, finite-domain expansion and the empty-domain convention. Equivalences are checked on every model with up to three elements.
A partial preview of the top of the sheet. The full sheet is in the Engineering Mathematics cheat sheet pack.
