1. List the elements in the set S = {n\n e N and n! = 7} 2. State whether this statement is TRUE or FALSE (justify your answer).13 € {3x+10| x € N} 3. Let A={X, Y, Z} and B={1,2,3, 4, 5}. What is |P(A × B)|? (P denotes the power set.)
1. List the elements in the set S = {n\n e N and n! = 7} 2. State whether this statement is TRUE or FALSE (justify your answer).13 € {3x+10| x € N} 3. Let A={X, Y, Z} and B={1,2,3, 4, 5}. What is |P(A × B)|? (P denotes the power set.)
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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discrete mathematics
![### Transcription of Educational Content
1. **List the elements in the set \( S = \{ n | n \in \mathbb{N} \text{ and } n! = 7 \} \)**
2. **State whether this statement is TRUE or FALSE (justify your answer).**
\[
13 \in \{3x + 10 | x \in \mathbb{N} \}
\]
3. **Let \( A = \{ X, Y, Z \} \) and \( B = \{1, 2, 3, 4, 5\} \). What is \(|\mathcal{P} (A \times B)|\)? (\(\mathcal{P}\) denotes the power set.)**
4. **Let \( A, B, \) and \( C \) be sets. Using the laws of set theory, show that:**
\[
(B - A) \cup (C - A) = (B \cup C) - A
\]
5. **Pavement Coffeehouse conducted a survey to see what kinds of coffee its customers like most. Given the following responses, determine how many people responded to the survey:**
- 40 like espresso
- 37 like lattes
- 75 like iced coffee
- 19 like both espresso and iced coffee
- 13 like both espresso and lattes
- 10 like both iced coffee and lattes
- 4 like all three options
- 16 don’t like any of the options
This content includes basic set theory problems and a real-world application scenario using survey data. The problems cover elements of sets, power sets, and application of set laws, offering a comprehensive exercise in understanding and applying basic mathematical concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fc8942a-d9e4-4836-9950-e7394b1cdb91%2Ffed0798c-1055-4397-ad49-c90da0d1b1c1%2Ff8jye2e_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription of Educational Content
1. **List the elements in the set \( S = \{ n | n \in \mathbb{N} \text{ and } n! = 7 \} \)**
2. **State whether this statement is TRUE or FALSE (justify your answer).**
\[
13 \in \{3x + 10 | x \in \mathbb{N} \}
\]
3. **Let \( A = \{ X, Y, Z \} \) and \( B = \{1, 2, 3, 4, 5\} \). What is \(|\mathcal{P} (A \times B)|\)? (\(\mathcal{P}\) denotes the power set.)**
4. **Let \( A, B, \) and \( C \) be sets. Using the laws of set theory, show that:**
\[
(B - A) \cup (C - A) = (B \cup C) - A
\]
5. **Pavement Coffeehouse conducted a survey to see what kinds of coffee its customers like most. Given the following responses, determine how many people responded to the survey:**
- 40 like espresso
- 37 like lattes
- 75 like iced coffee
- 19 like both espresso and iced coffee
- 13 like both espresso and lattes
- 10 like both iced coffee and lattes
- 4 like all three options
- 16 don’t like any of the options
This content includes basic set theory problems and a real-world application scenario using survey data. The problems cover elements of sets, power sets, and application of set laws, offering a comprehensive exercise in understanding and applying basic mathematical concepts.
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