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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: Q9SE (page 187)

Suppose that A, B, and C are sets. Prove or disprove that $(A - B) - (C - D) = (A - C) - (B - D)$

Short Answer

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$(A - B) - (C - D) = (A - C) - (B - D)$

Step by step solution

Step: 1

No, For example, let $A = B = \{a, b\}$ , $C = \emptyset$ and role="math" localid="1668428238907" $D = \{a\}$ . Then $(A - B) - (C - D) = \emptyset - \emptyset = \emptyset$ butrole="math" localid="1668428272716" $(A - C) - (B - D) = \{a, b\} - \{b\} = \{a\}$

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Most popular questions from this chapter

Question:

a. Give an example to show that the inclusion in part (b) in exercise 40 may be proper.

b.Show that if f is one-to-one, the inclusion in part(b) in exercise 40 is an equality.

a) define the floor and ceiling functions from the set of real numbers to the set of integers.

b) For which real numbersis it true that $[x] = ⌈ x ⌉$

Let $S = {- 1, 0, 2, 4.7}$ . Find f(S) if

role="math" localid="1668419106110" $f (x) = 1$
role="math" localid="1668419096298" $f (x) = 2 + 1$
role="math" localid="1668419089300" $f (x) = [x / 5]$
$f (x) = [(x^{2} + 1) / 3]$

Prove that if x is a positive real number, then

$\begin{aligned} (a) ⌊ \sqrt{⌊ x ⌋} ⌋ = ⌊ \sqrt{x} ⌋ \\ (b) [\sqrt{⌊ x ⌋}] = ⌈ \sqrt{x} ⌉ \end{aligned}$

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 $(f \circ g)^{- 1} = g^{- 1} \circ f^{- 1}$

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Suppose that A, B, and C are sets. Prove or disprove that $(A - B) - (C - D) = (A - C) - (B - D)$

Short Answer

Step by step solution

Step: 1

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Suppose that A, B, and C are sets. Prove or disprove that(A-B)-(C-D)=(A-C)-(B-D)

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

Geometry

Applied Mathematics

Discrete Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Suppose that A, B, and C are sets. Prove or disprove that $(A - B) - (C - D) = (A - C) - (B - D)$