If a set is defined as {x | x is a natural number and x < 10}, which of the f

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Question: If a set is defined as {x | x is a natural number and x < 10}, which of the following is the correct representation of this set?

Options:

Correct Answer: {1, 2, 3, 4, 5, 6, 7, 8, 9}

Solution:

The correct representation of the set is {1, 2, 3, 4, 5, 6, 7, 8, 9}, as it includes all natural numbers less than 10.

If a set is defined as {x | x is a natural number and x < 10}, which of the following is the correct representation of this set?

If a set is defined as {x | x is a natural number and x < 10}, which of the following is the correct representation of this set?

Step 1: Understand what a natural number is. Natural numbers are the positive integers starting from 1 (1, 2, 3, ...).
Step 2: Identify the condition given in the set definition, which is 'x < 10'. This means we are looking for natural numbers that are less than 10.
Step 3: List the natural numbers starting from 1 and stop before reaching 10. The numbers are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Step 4: Combine these numbers into a set format. The set is represented as {1, 2, 3, 4, 5, 6, 7, 8, 9}.
Step 5: Confirm that this set includes all natural numbers less than 10, which matches the condition given.

Set Notation – Understanding how to interpret and represent sets using set-builder notation.
Natural Numbers – Knowledge of what constitutes natural numbers and their properties.
Inequalities – Ability to understand and apply inequalities in the context of set definitions.