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Elementary Notions and Notations |
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1 | (73) |
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2 | (11) |
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2 | (3) |
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5 | (1) |
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6 | (6) |
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12 | (1) |
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13 | (22) |
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13 | (5) |
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18 | (8) |
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26 | (3) |
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29 | (1) |
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Sets Should Not Be Too Complicated |
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30 | (1) |
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31 | (4) |
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35 | (20) |
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35 | (4) |
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39 | (2) |
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41 | (5) |
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46 | (3) |
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49 | (3) |
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52 | (3) |
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55 | (17) |
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55 | (4) |
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59 | (2) |
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61 | (2) |
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63 | (5) |
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68 | (2) |
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70 | (2) |
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72 | (1) |
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73 | (54) |
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74 | (17) |
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74 | (5) |
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79 | (8) |
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87 | (1) |
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88 | (3) |
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91 | (9) |
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91 | (5) |
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96 | (2) |
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98 | (2) |
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100 | (15) |
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Injections and Surjections |
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100 | (2) |
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102 | (3) |
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105 | (1) |
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106 | (3) |
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109 | (2) |
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111 | (4) |
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115 | (10) |
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Comparing the Size of Sets |
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115 | (1) |
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116 | (3) |
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119 | (2) |
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121 | (3) |
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124 | (1) |
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125 | (2) |
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127 | (66) |
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128 | (17) |
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129 | (3) |
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132 | (2) |
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134 | (4) |
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138 | (2) |
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Cartesian Products of Sets |
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140 | (2) |
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142 | (3) |
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Recursive Functions and Procedures |
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145 | (28) |
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146 | (4) |
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150 | (3) |
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153 | (6) |
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159 | (4) |
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163 | (2) |
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165 | (3) |
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168 | (5) |
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173 | (18) |
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Recalling English Grammar |
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173 | (1) |
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174 | (3) |
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177 | (4) |
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181 | (5) |
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186 | (2) |
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188 | (3) |
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191 | (2) |
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Equivalence, Order, and Inductive Proof |
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193 | (80) |
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Properties of Binary Relations |
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194 | (19) |
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195 | (4) |
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199 | (5) |
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204 | (5) |
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209 | (4) |
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213 | (19) |
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214 | (4) |
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218 | (1) |
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219 | (6) |
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Generating Equivalence Relations |
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225 | (4) |
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229 | (3) |
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232 | (21) |
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233 | (6) |
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239 | (3) |
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242 | (8) |
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250 | (1) |
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251 | (2) |
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253 | (19) |
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Proof by Mathematical Induction |
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253 | (6) |
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Proof by Well-Founded Induction |
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259 | (2) |
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261 | (6) |
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267 | (5) |
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272 | (1) |
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273 | (72) |
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274 | (7) |
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274 | (3) |
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277 | (4) |
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281 | (1) |
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281 | (8) |
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282 | (5) |
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287 | (2) |
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Counting and Discrete Probability |
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289 | (23) |
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Permutations (Order Is Important) |
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289 | (4) |
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Combinations (Order Is Not Important) |
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293 | (5) |
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298 | (11) |
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309 | (3) |
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312 | (22) |
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Solving Simple Recurrences |
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313 | (6) |
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319 | (13) |
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332 | (2) |
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Comparing Rates of Growth |
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334 | (8) |
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334 | (4) |
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338 | (1) |
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339 | (2) |
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341 | (1) |
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342 | (3) |
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345 | (52) |
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346 | (2) |
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347 | (1) |
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How Can We Tell Whether Something Is a Proof? |
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348 | (1) |
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348 | (21) |
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Well-Formed Formulas and Semantics |
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349 | (4) |
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353 | (5) |
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Truth Functions and Normal Forms |
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358 | (7) |
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Complete Sets of Connectives |
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365 | (2) |
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367 | (2) |
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369 | (15) |
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370 | (2) |
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372 | (8) |
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380 | (1) |
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381 | (3) |
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384 | (10) |
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384 | (7) |
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391 | (1) |
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392 | (2) |
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394 | (3) |
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397 | (60) |
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First-Order Predicate Calculus |
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397 | (19) |
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Predicates and Quantifiers |
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398 | (4) |
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402 | (2) |
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Semantics and Interpretations |
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404 | (5) |
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409 | (4) |
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413 | (1) |
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413 | (3) |
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416 | (16) |
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416 | (8) |
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424 | (3) |
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Formalizing English Sentences |
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427 | (2) |
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429 | (1) |
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430 | (2) |
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Formal Proofs in Predicate Calculus |
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432 | (24) |
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Universal Instantiation (UI) |
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433 | (4) |
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Existential Generalization (EG) |
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437 | (1) |
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Existential Instantiation (EI) |
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438 | (2) |
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Universal Generalization (UG) |
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440 | (3) |
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Examples of Formal Proofs |
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443 | (7) |
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Summary of Quantifier Proof Rules |
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450 | (1) |
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451 | (5) |
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456 | (1) |
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457 | (48) |
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458 | (8) |
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458 | (6) |
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Extending Equals for Equals |
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464 | (1) |
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465 | (1) |
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466 | (25) |
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Imperative Program Correctness |
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467 | (11) |
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478 | (4) |
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482 | (4) |
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486 | (5) |
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491 | (12) |
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Classifying Higher-Order Logics |
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492 | (4) |
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496 | (2) |
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498 | (3) |
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501 | (2) |
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503 | (2) |
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505 | (52) |
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505 | (28) |
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Clauses and Clausal Forms |
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506 | (6) |
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Resolution for Propositions |
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512 | (2) |
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Substitution and Unification |
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514 | (7) |
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Resolution: The General Case |
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521 | (5) |
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Theorem Proving with Resolution |
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526 | (3) |
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529 | (1) |
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530 | (3) |
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533 | (22) |
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534 | (2) |
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Definition of a Logic Program |
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536 | (1) |
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Resolution and Logic Programming |
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537 | (12) |
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Logic Programming Techniques |
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549 | (4) |
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553 | (2) |
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555 | (2) |
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Algebraic Structures and Techniques |
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557 | (76) |
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558 | (14) |
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560 | (2) |
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562 | (2) |
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564 | (6) |
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570 | (2) |
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572 | (13) |
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Simplifying Boolean Expressions |
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574 | (4) |
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578 | (5) |
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583 | (2) |
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Abstract Data Types as Algebras |
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585 | (16) |
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585 | (4) |
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589 | (3) |
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592 | (4) |
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Binary Trees and Priority Queues |
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596 | (3) |
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599 | (2) |
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601 | (12) |
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601 | (6) |
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607 | (4) |
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611 | (2) |
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613 | (19) |
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613 | (3) |
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Cryptology: The RSA Algorithm |
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616 | (5) |
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621 | (2) |
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623 | (6) |
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629 | (3) |
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632 | (1) |
Answers to Selected Exercises |
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633 | (74) |
Bibliography |
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707 | (4) |
Greek Alphabet |
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711 | (2) |
Symbol Glossary |
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713 | (6) |
Index |
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719 | |