By Thomas Koshy

ISBN-10: 0124211801

ISBN-13: 9780124211803

This approachable textual content experiences discrete items and the relationsips that bind them. It is helping scholars comprehend and follow the facility of discrete math to electronic desktops and different glossy purposes. It offers very good training for classes in linear algebra, quantity idea, and modern/abstract algebra and for machine technological know-how classes in information buildings, algorithms, programming languages, compilers, databases, and computation.

* Covers all instructed themes in a self-contained, complete, and comprehensible structure for college kids and new pros

* Emphasizes problem-solving recommendations, trend popularity, conjecturing, induction, purposes of various nature, evidence suggestions, set of rules improvement and correctness, and numeric computations

* Weaves a number of functions into the text

* is helping scholars research by way of doing with a wealth of examples and exercises:

- 560 examples labored out in detail

- greater than 3,700 exercises

- greater than one hundred fifty desktop assignments

- greater than six hundred writing projects

* comprises bankruptcy summaries of vital vocabulary, formulation, and homes, plus the bankruptcy evaluate exercises

* beneficial properties attention-grabbing anecdotes and biographies of 60 mathematicians and computing device scientists

* Instructor's handbook on hand for adopters

* pupil suggestions guide to be had individually for buy (ISBN: 0124211828)

**Read Online or Download Discrete Mathematics with Applications PDF**

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**Additional info for Discrete Mathematics with Applications**

**Example text**

While ∼[(x = y) ∨ (y = z)] do 25. While ∼[(x = 6) ∨ (y = z)] do c←c+1 c←c+1 The logical operators NAND (not and) and NOR (not or) are deﬁned as follows: p NAND q ≡ ∼( p ∧ q) p NOR q ≡ ∼(p ∨ q) Construct a truth table for each proposition. 26. p NAND q 27. p NOR q Mark each sentence as true or false, where p, q, and r are arbitrary statements, t a tautology, and f a contradiction. 28. p ∧ q ≡ q ∧ p 29. p ∨ q ≡ q ∨ p 30. p ∧ t ≡ p 31. p ∨ f ≡ p 32. p ∨ ∼p ≡ t 33. p ∧ ∼p ≡ f 34. ∼( p ∧ q) ≡ ∼p ∧ ∼q 35.

26 The absolute value of a real number x, denoted by |x|, is deﬁned by |x| = ⎧ ⎨x if x ≥ 0 ⎩ −x if x < 0 Determine the truth value of each proposition, where the UD = set of all real numbers: (1) (∀x) (x2 ≥ 0) (2) (∀x) (|x| > 0) SOLUTION: (1) Since the square of every real number is nonnegative, the truth value of (∀x) (x2 ≥ 0) is T. (2) It is not true that the absolute value of every number is positive, since |0| = 0, not greater than zero. So the truth value of (∀x) (|x| > 0) is F. A predicate may contain two or more variables.

2. p ≡ q, q ≡ r, and r is true. Verify each, where f denotes a contradiction. ) 3. ∼(∼p) ≡ p 4. p ∧ p ≡ p 5. p ∨ p ≡ p 6. p ∧ q ≡ q ∧ p 7. p ∨ q ≡ q ∨ p 8. ∼( p ∨ q) ≡ ∼p ∧ ∼q 9. ∼( p → q) ≡ p ∧ ∼q 30 Chapter 1 The Language of Logic 10. p → q ≡ ( p ∧ ∼q) → f 11. p ∧ (q ∧ r) ≡ (p ∧ q) ∧ r 12. p → (q ∨ r) ≡ ( p ∧ ∼q) → r 13. ( p ∨ q) → r ≡ ( p → r) ∧ (q → r) Use De Morgan’s laws to evaluate each boolean expression, where x = 2, y = 5, and z = 3. 14. ∼[(x < z) ∧ (y < z)] 15. ∼[(y < x) ∧ (z < x)] 16.

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