Graph ›
Part II ›
Logic, Sets, and Maps
Logic, Sets, and Maps
foundations +45 more results +16 more equations depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) definition 3.1: Logical proposition 3.1 Logical proposit… definition 3.2: Axiom 3.2 Axiom definition 3.3: Theorem 3.3 Theorem definition 3.4: Theory 3.4 Theory definition 3.5: Logical operator 3.5 Logical operator definition 3.6: Truth table 3.6 Truth table definition 3.7: Negation 3.7 Negation definition 3.8: Conjunction 3.8 Conjunction definition 3.9: Disjunction 3.9 Disjunction definition 3.10: Exclusive disjunction 3.10 Exclusive disjun… definition 3.11: Conditional 3.11 Conditional definition 3.12: Biconditional 3.12 Biconditional definition 3.13: Logical expression 3.13 Logical expressi… proposition 3.19: Conditional as disjunction 3.19 Conditional as d… proposition 3.20: De Morgan's laws 3.20 De Morgan's laws proposition 3.21: Contraposition 3.21 Contraposition proposition 3.22: Algebra of propositions 3.22 Algebra of propo… proposition 3.37: De Morgan's laws for sets 3.37 De Morgan's laws… proposition 3.42: Cardinal of the power set 3.42 Cardinal of the… proposition 3.48: Characterization of bijectivity 3.48 Characterization… proposition 3.54: Preimages respect the set operations 3.54 Preimages respec… proposition 3.56: Composition is associative 3.56 Composition is a… proposition 3.57: Composition of bijective maps 3.57 Composition of b… theorem 3.60: Equivalence classes partition the set 3.60 Equivalence clas… proposition 3.63: prop:inf-equipotence-equivalence 3.63 proposition proposition 3.67: Countability of the plane of naturals 3.67 Countability of… equation 3.3: eq:log-negation eq. (3.3) equation 3.10: eq:log-conditional eq. (3.10) equation 3.15: eq:log-demorgan-and eq. (3.15) equation 3.16: eq:log-demorgan-or eq. (3.16) equation 3.25: eq:log-excluded-middle eq. (3.25) equation 3.26: eq:log-noncontradiction eq. (3.26) equation 3.47: eq:set-double-inclusion eq. (3.47) equation 3.51: eq:set-indexed eq. (3.51) equation 3.76: eq:inf-Z-bijection eq. (3.76) equation 3.86: eq:provability-predicate eq. (3.86) equation 3.89: eq:goedel-sentence eq. (3.89) equation 3.90: eq:con-sentence eq. (3.90) The chain of Logic, Sets, and Maps: 38 of 99 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.