Solved on Jan 19, 2024

Find the set of counting numbers less than or equal to 3, expressed using set notation and listing method. {1,2,3}\{1, 2, 3\}

STEP 1

Assumptions
1. Counting numbers are the positive integers starting from 1.
2. The set includes all counting numbers less than or equal to 3.

STEP 2

Identify the first counting number.
Counting numbers start from 1.

STEP 3

List all counting numbers starting from 1 up to and including 3.
The counting numbers less than or equal to 3 are 1, 2, and 3.

STEP 4

Express the set using set notation.
The set notation for the counting numbers less than or equal to 3 is:
{xNx3}\{x \in \mathbb{N} \mid x \leq 3\}

STEP 5

Use the listing method to describe the set.
The set can be listed as:
{1,2,3}\{1, 2, 3\}

STEP 6

Combine the set notation and the listing method to fully describe the set.
The set of all counting numbers less than or equal to 3 is:
{xNx3}={1,2,3}\{x \in \mathbb{N} \mid x \leq 3\} = \{1, 2, 3\}

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