Page 395 - HOW TO PROVE IT: A Structured Approach, Second Edition

P1: Oyk/
0521861241ind CB996/Velleman October 20, 2005 4:19 0 521 86124 1 Char Count= 0

Index

absorption laws, 21 composition, 177, 178, 182, 231, 300
antecedent, 44 conclusion, 8, 85
antisymmetric, 189 conditional
arbitrary object, 108 antecedent of, 44
arithmetic mean, 276 consequent of, 44
arithmetic-geometric mean inequality, 276 laws, 44–45, 47, 50
associative laws, 22, 23 truth table for, 44–45, 47
for ∧ and ∨, 21, 25 congruent, 213
asymmetric, 210 conjecture, 2
conjunction, 10
base case, connective symbol, 10
Bernstein, Felix, 322 consequent, 44
biconditional, 23, 52, 53 constant function, 235, 244
truth table for, 23, 52 continuum hypothesis, 326–327
big-oh, 235 contradiction, 22, 23, 26, 32, 41
bijection, 182, 242 law, 23
binary relation, 182, 242 proof by, 96, 97, 98, 99
binomial coefficient, 288 contrapositive, 49, 91
binomial theorem, 260, 288 law, 49
bound variable, 29 converse, 49
bounded quantifier, 57, 68 coordinate, 163
countable set, 310
Canter’s Theorem, 318, 320, 321 counterexample, 2, 85
Cantor, Georg, 318
Cantor-Schr¨oder-Bernstein Theorem, DeMorgan’s law, 20, 21, 22, 23, 25, 39, 47, 50
322–327 denumerable set, 318, 326
cardinality, 307 diagonalization, 320
Cartesian product, 163–171 difference of sets, 34
cases, 136 directed graph, 183
closure disjoint, 40
reflexive, 202 pairwise, 153, 214
reflexive symmetric, 212 disjunction, 10
of a set under a function, 303 disjunctive syllogism, 142
symmetric, 204, 205 distributive laws, 38–39
symmetric transitive, 212 for ∃,70
transitive, 204, 209, 300 for ∀ and ∨,70
Cohen, Paul, 327 for ∩ and ∪, 38–39
commutative laws for ∧ and ∨, 21, 23, 52 for ∧ and ∨, 21, 23
compatible, 225, 236 divides, 121

381