MATH 1240 W2022 Suggested Practice Problems
TEXT: . Grimaldi, Discrete and combinatorial mathematics, an applied introduction, 5th ed., , Inc., 2004.
Sect Grimaldi Pg
1.1 2.1 Basic Connectives and Truth Tables 54
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1.2 2.2 Logical Equivalence: The Laws of Logic 66
1.3 2.3 Logical Implication: Rules of Inference 84
1.4 2.4 The Use of Quantifiers 100
1.5 2.5 Quantifiers, Definitions, and Proofs 116
1.6 4.1 Mathematical Induction 208
1.7 4.2 Recursive Definitions 219
Ch4 Supplemental 245
2.1 3.1 Sets and Subsets 134
2.2 3.2 Set Operations, Laws of Set Theory 146
Ch3 Supplemental 189
3.1 4.3 The Division Algorithm 230
3.2 4.4 GCD / Euclidean Algorithm 236
3.3 4.5 Fundamental Theorem of Arithmetic 240
Ch4 Supplemental 245
4.1–2 1.1 Rules of Sum and Product & 1.2 Per- 11
4.3 1.3 Combinations: The Binomial Theorem 24
4.4 3.3 Counting and 150
Ch3 Supplemental 189
5.1 11.1 An Introduction to Graph Theory 518 7.2 Digraphs 354 11.2 Subgraphs, Complements, and Graph 528
Isomorphism
5.2 11.3 Vertex Degree: Euler Trails and Cir- 537
5.3 11.4 Planar Graphs 553
5.4 11.5 Hamilton Paths and Cycles 562
5.5 11.6 Graph Colouring and Chromatic Poly- 571
Ch11 Supplemental 576
5.6 12.1 Trees: Definitions, Properties, Exam- 585
Suggested Homework
1, 3, 4, 5abd, 6ab, 7, 8aeg, 15, try 17
1, 5, 6, 7a, 9, 10, 11, 13, 14a
4, 5, 8, 10, 11ac, 12ac
1, 3, 5, 8, 9, 11, 13-18, 21, 23, 25, try 26
1ac, 2a, 11ab, 15, 19, 23a, 24b
1bce, 11, 12
1-7, 10, 15, 18
1, 3a, 5, 7a, 8, 13, 17ac, 19
2, 3-5, 9, 14, 15, 16, 17, 18
1,2,5,10,13
1,3,5,13,17,try25,do27
4,5,7a,try8,do15,25b 1,3,5,7,11ab,13,15,19,21,23,try29,do31,33,35,37; 4.5 #7
1,3,5, 6,7,8,9,13,15,19,21,23,27,29,31,32,33 1,3,4, 5,try9
2, 4b, 5a, 8,10, 15, 17-20, 23a
2,3,5,6,7,9,10,12a
15, 16, 20, 21, 24, 27
1ade, 3b, 4-6, 9-11, 14a
1,2,3,5,6,8,9a,10,13,14,19a,20,21,23,29,35
2-9, 12-14, 17
1-3, 7a, 18
1-4, 7, 8, 9b, 19ab
1, 5, 6, 7, 8abd, 15bc, 16a, 22 1,3,4,5,7,try9,do11,13
1-7, 8ac, 9, 15-17, try 18, 21 and 27 1,3,4,7
1, 3-9, 11, 12
1-7, 11, 12, 15, 19, 20, 24
1, 3-5, 7-10, 12, 14, 17, 18abc, 20-22
2, 3, 6, 9a, 10, 12-15, 19a, 24, 25a, 27, 28ab, 30, 31, 32a, 33a
1-5, 7, 10, 12
1, 5-11, 13-14, 16-17 1,2,7a,10,11,13,15,17,18,25
1,3,6,9,13
1, 3-8, 10[proof of 14.11 only], 13, 18b, 22a, 29
Functions: Plain and One-to-one 258 Onto Functions: 265 Special Functions 272 The Pigeonhole Principle 277
Function Composition and Inverse 288 Functions
Ch5 Supplemental 305
7 A3 Countable and Uncountable Sets A-32
8.1 5.1 Cartesian Products and Relations 252 Ch 5 Supplemental 305
8.2 7.1 Relations Revisited 343
8.3 7.3 Partial Orders: 364
8.4 7.4 Equivalence Relations 370
8.5 14.3 The Integers Modulo n 696
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