Use set notation and write the elements belonging to the set {x | x is a natural number less than 6}.

Verified step by step guidance

1. Understand the set notation given: \(\{x \mid x \text{ is a natural number less than } 6\}\) means the set of all natural numbers \(x\) such that \(x\) is less than 6.
2. Recall that natural numbers are the positive integers starting from 1, so the natural numbers less than 6 are 1, 2, 3, 4, and 5.
3. List these numbers explicitly as elements of the set using set notation with curly braces: \(\{1, 2, 3, 4, 5\}\).
4. Verify that each element in the set satisfies the condition of being a natural number less than 6.
5. Write the final answer as the set of elements: \(\{1, 2, 3, 4, 5\}\).

Key Concepts

Set Notation

Set notation is a mathematical way to describe a collection of elements. It often uses curly braces {} to list elements or a rule to define membership, such as {x | condition on x}. This notation helps clearly specify which elements belong to the set.

Natural Numbers

Natural numbers are the set of positive integers starting from 1, often used for counting. In some contexts, zero is included, but typically natural numbers are {1, 2, 3, ...}. Understanding this helps identify which numbers satisfy the given condition.

Inequalities and Set Builder Notation

Inequalities express conditions like 'less than 6' to restrict elements in a set. Set builder notation uses these inequalities to define sets by specifying properties elements must satisfy, such as {x | x < 6}, meaning all x less than 6.