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

검증된 단계별 안내

Understand the set notation: {x | x is a natural number less than 3} means the set of all natural numbers x such that x is less than 3.

Recall the definition of natural numbers: natural numbers are typically the positive integers starting from 1, i.e., {1, 2, 3, 4, ...}.

Identify all natural numbers less than 3: these are 1 and 2, since both are natural numbers and both are less than 3.

Write the set explicitly: {x | x is a natural number less than 3} = {1, 2}.

Compare this with the given set {1, 2} and conclude that the statement is true because both sets contain exactly the same elements.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Set Notation

Set notation is a way to describe a collection of elements using curly braces {}. The vertical bar '|' means 'such that,' and it specifies a condition that elements must satisfy to be included in the set. For example, {x | x is a natural number less than 3} describes all natural numbers x that are less than 3.

Natural Numbers

Natural numbers are the set of positive integers starting from 1, 2, 3, and so on. They do not include zero or negative numbers. Understanding what counts as a natural number is essential when interpreting sets defined by conditions involving natural numbers.

Set Equality

Two sets are equal if and only if they contain exactly the same elements. Order and repetition do not matter in sets. To determine if {x | x is a natural number less than 3} equals {1, 2}, we check if both sets have the same elements without any extras.