By Kevin Ferland

ISBN-10: 0618415386

ISBN-13: 9780618415380

Discrete arithmetic combines a stability of concept and functions with mathematical rigor and an available writing kind. the writer makes use of more than a few examples to educate middle thoughts, whereas corresponding workouts let scholars to use what they study. during the textual content, attractive anecdotes and issues of curiosity tell in addition to encourage beginners. The textual content is perfect for one- or two-semester classes and for college students who're in general arithmetic, arithmetic schooling, or desktop technological know-how majors. half I teaches pupil how one can write proofs; half II specializes in computation and challenge fixing. the second one half the booklet can also be appropriate for introductory classes in combinatorics and graph conception.

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**Extra resources for Discrete Mathematics: An Introduction to Proofs and Combinatorics**

**Sample text**

62. ( p ∨ q ) ∧ ( p ∨ q ∨ r ) ≡ p ∨ q . 63. Show that the operation ¬, together with any one of the operations ∧, ∨, and →, can be used to generate the other two. 10 accomplishes part of this. 64. Can the operation ∨ be generated from the operations ⊕, ¬, and ∧? Explain. In Exercises 65 through 68: (a) Trace the pictured circuit to determine an expression for the output in terms of the input. (b) Make an input-output table. ∗ Exercises that may be particularly challenging are marked with a star.

9 Interval Notation Given real numbers a and b, we deﬁne the following intervals. 9 is actually not complete. For example, the set description of the interval (a , b) should more precisely be {x : x ∈ R and a < x < b}. 9: that x represents a real number. 9, it is assumed that we are working in the context of the set of real numbers, although that is not explicitly stated. Implicitly assuming a certain context is common in mathematical notation. When we work with a collection of sets, it is often the case that all of those sets are subsets of some bigger set called the universal set (or universe of consideration) for that particular context.

32. {9} {9, {9, 10}}. 33. {3} {3, {3}, {{3}}}. 34. {4, 5} {{4}, {5}}. In Exercises 35 through 42, determine whether the given set is ﬁnite or inﬁnite. If it is ﬁnite, then ﬁnd its cardinality. 35. A = {1, 3, 5, 7, 9}. 36. B = {x : x ∈ R and x4 = 16}. 37. C = [5, 6]. 39. E = {n : n ∈ N and n ≤ 8}. 38. D = {x : x ∈ R and x 2 > 2}. 40. F = {n : n ∈ Z− and n ≤ 12 }. 41. G = {∅, {∅}}. 42. H = {{{∅}}}. In Exercises 43 and 44, discover a paradox by trying to answer the included question. 43. Barber Puzzle.

### Discrete Mathematics: An Introduction to Proofs and Combinatorics by Kevin Ferland

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