Question

Express the following set using set-builder notation:
x ∈ N and 17 < x < 24.

Answer 1

The set x expressed in set-builder notation is: {x ∈ N : 17 < x < 24}.

Step-by-step explanation:

Set-builder notation is a concise way to represent a set by describing the characteristics or properties its elements must satisfy. In this case, the given set consists of natural numbers (N) that fall within the range of numbers greater than 17 but less than 24.

The notation x can be expressed more compactly as {x ∈ N : 17 < x < 24}. Here, the symbol "∈" denotes "belongs to" or "is an element of," and the colon ":" signifies "such that."

The set {x ∈ N : 17 < x < 24} represents all natural numbers (x) that meet the condition of being greater than 17 and less than 24. Natural numbers are positive integers starting from 1, 2, 3, and so on. Therefore, the set-builder notation {x ∈ N : 17 < x < 24} describes the collection of natural numbers within the specified range, excluding 17 and 24 themselves. The set includes numbers 18, 19, 20, 21, 22, and 23.

Set-builder notation provides a clear and concise way to define a set based on specific criteria or conditions, making it easier to comprehend and represent a set of elements that fulfill certain properties or requirements.

Answer 2

The set x can be expressed in set-builder notation as:

{ x | x ∈
`\mathbb{N}`, 17 < x < 24 }

Step-by-step explanation:

Set-builder notation is a way to represent a set by describing its elements based on certain properties or conditions. In this case, the set x ∈ N and 17 < x < 24 denotes all natural numbers greater than 17 and less than 24.

The expression { x | x ∈
`\mathbb{N}`, 17 < x < 24 } reads as "the set of all x such that x belongs to the set of natural numbers
`\mathbb{N}` and x lies between 17 and 24, excluding both boundaries."

The symbol
`\mathbb{N}` represents the set of natural numbers, which includes positive integers starting from 1 (1, 2, 3, ...) and continuing indefinitely. The condition (17 < x < 24) specifies that the set includes natural numbers greater than 17 but less than 24, implying that the elements of the set are 18, 19, 20, 21, 22, and 23.

Therefore, the set-builder notation { x | x ∈
`\mathbb{N}`, 17 < x < 24 } precisely defines the set containing natural numbers that satisfy the specified conditions, offering a concise and mathematical way to describe the set's elements based on its defining properties.