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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 2: Q11SE (page 187)

Let A and B be sets in a finite universal set U. List the following in order of increasing size.
a) $| A |, | A \cup B |, | A \cap B |, | U |, | \emptyset |$
b)

Short Answer

Expert verified

a) $| \emptyset | \leq | A \cap B | \leq | A | \leq | A \cup B | \leq | U |$

b) $| \emptyset | \leq | A - B | \leq | A \oplus B | \leq | A \cup B | \leq | A | + | B |$

Step by step solution

Step: 1

a) $| \emptyset | \leq | A \cap B | \leq | A | \leq | A \cup B | \leq | U |$

b) $| \emptyset | \leq | A - B | \leq | A \oplus B | \leq | A \cup B | \leq | A | + | B |$

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Most popular questions from this chapter

For each of these partial functions, determine its domain, codomain, domain of definition, and the set of values for which it is undefined. Also, determine whether it is a total function.

$\begin{aligned} (a) f : Z \to R, f (n) = 1 / n \\ (b) f : Z \to Z, f (n) = ⌈ n / 2 ⌉ \\ (c) f : Z \times Z \to Q, f (m, n) = m / n \\ (d) f : Z \times Z \to Z, f (m, n) = mn \\ (e) f : Z \times Z \to Z, f (m, n) = m - nifm > n \end{aligned}$

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a) define the union, intersection, difference, and symmetric difference of two sets.

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Let A and B be sets in a finite universal set U. List the following in order of increasing size.
a) $| A |, | A \cup B |, | A \cap B |, | U |, | \emptyset |$
b)

Short Answer

Step by step solution

Step: 1

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Let A and B be sets in a finite universal set U. List the following in order of increasing size.a)|A|,|A∪B|,|A∩B|,|U|,|∅|b)

Short Answer

Step by step solution

Step: 1

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Let A and B be sets in a finite universal set U. List the following in order of increasing size.
a) $| A |, | A \cup B |, | A \cap B |, | U |, | \emptyset |$
b)