Determine whether each statement is true or false. {x | x is a natural number less than 3}= {1, 2}

Verified step by step guidance

1. Identify the set of natural numbers less than 3.
2. Natural numbers are positive integers starting from 1.
3. List the natural numbers less than 3: 1 and 2.
4. Compare the set {x | x is a natural number less than 3} with the set {1, 2}.
5. Determine if both sets contain the same elements.

Key Concepts

Natural Numbers

Natural numbers are the set of positive integers starting from 1 and going upwards (1, 2, 3, ...). They do not include zero or any negative numbers. Understanding this concept is crucial for determining the elements of the set in the question.

Set Notation

Set notation is a mathematical way to describe a collection of objects, often using curly braces. The notation {x | condition} defines a set of elements x that satisfy a specific condition. In this case, it specifies natural numbers less than 3.

Set Equality

Set equality occurs when two sets contain exactly the same elements, regardless of the order or repetition of those elements. To determine if the statement is true or false, one must compare the defined set with the given set {1, 2} to see if they are identical.