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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

Question: Let $f : R \to R$ and $f (x) > 0$ let for all $x \in R$ . Show that f(x) is strictly increasing if and only if the function $g (x) = 1 / f (x)$ is strictly decreasing.

a) Explain what it means for two sets to be equal.

b) Describe as many of the ways as you can to show that two sets are equal.

c) Show in at least two different ways that the sets $A - (B \cap C)$ and $(A - B) \cup (A - C)$

Suppose that f is an invertible function from Y to Z and g is an invertible function from X to Y. Show that the inverse of the composition f $\circ$ g is given by $(f \circ g)^{- 1} = g^{- 1} \circ f^{- 1}$

explain what it means for one set to be a subset of another set. How do you prove that one set is a subset of another set?

Question: Specify a codomain for each of the functions in Exercise 17. Under what conditions is each of the functions with the codomain you specified onto?

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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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Most popular questions from this chapter

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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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

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)