please give me the correct answer and explain how to do this. ### Set Membership Problem#### Problem Statement:Select all of the following that are members of the set:\[\left\{ a \in \mathbb{N} : a^2 - 1 \text{ is divisible by } 4 \right\} \times \left\{ b \in \mathbb{Z} : b \text{ is prime} \right\}\]#### Choices:- [ ] (3, 7)- [ ] (8, 18)- [ ] (5, 5)- [ ] (7, 8)- [ ] (1, 2)- [ ] (6, 2)#### Explanation:1. **First set (Natural numbers):** - The elements \(a\) in the first set must satisfy the condition that \(a^2 - 1\) is divisible by 4. - To determine if a number \(a\) fits this condition, substitute \(a\) into the expression \(a^2 - 1\) and check if it is divisible by 4.2. **Second set (Integers):** - The elements \(b\) in the second set must be prime numbers. - A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.#### Detailed Evaluation:- **(3, 7):** - For \(a = 3\), \(3^2 - 1 = 9 - 1 = 8\), which is divisible by 4. - 7 is a prime number. - Thus, (3, 7) is a member of the set. - **(8, 18):** - For \(a = 8\), \(8^2 - 1 = 64 - 1 = 63\), which is not divisible by 4. - 18 is not a prime number. - Thus, (8, 18) is not a member of the set. - **(5, 5):** - For \(a = 5\), \(5^2 - 1 = 25 - 1 = 24\), which is divisible by 4. - 5 is a prime number. - Thus, (5, 5) is a member of

Sets are represented as a collection of well defined elements and these sets may be mathematical or…

Answered: Select all of the following that are…

Select all of the following that are members of this set: {a €N: a² - 1 is divisible by 4} × {b € Z: bis prime} (3,7) (5,5) (1,2) (8, 18) (7,8) (6,2)

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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Question

please give me the correct answer and explain how to do this.

### Set Membership Problem

#### Problem Statement:
Select all of the following that are members of the set:

\[
\left\{ a \in \mathbb{N} : a^2 - 1 \text{ is divisible by } 4 \right\} \times \left\{ b \in \mathbb{Z} : b \text{ is prime} \right\}
\]

#### Choices:
- [ ] (3, 7)
- [ ] (8, 18)
- [ ] (5, 5)
- [ ] (7, 8)
- [ ] (1, 2)
- [ ] (6, 2)

#### Explanation:
1. **First set (Natural numbers):**
- The elements \(a\) in the first set must satisfy the condition that \(a^2 - 1\) is divisible by 4.
- To determine if a number \(a\) fits this condition, substitute \(a\) into the expression \(a^2 - 1\) and check if it is divisible by 4.

2. **Second set (Integers):**
- The elements \(b\) in the second set must be prime numbers.
- A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

#### Detailed Evaluation:
- **(3, 7):**
- For \(a = 3\), \(3^2 - 1 = 9 - 1 = 8\), which is divisible by 4.
- 7 is a prime number.
- Thus, (3, 7) is a member of the set.

- **(8, 18):**
- For \(a = 8\), \(8^2 - 1 = 64 - 1 = 63\), which is not divisible by 4.
- 18 is not a prime number.
- Thus, (8, 18) is not a member of the set.

- **(5, 5):**
- For \(a = 5\), \(5^2 - 1 = 25 - 1 = 24\), which is divisible by 4.
- 5 is a prime number.
- Thus, (5, 5) is a member of

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