If set C = {x | x is a multiple of 3 and less than 30}, how many elements are in

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Question: If set C = {x | x is a multiple of 3 and less than 30}, how many elements are in set C?

Options:

Correct Answer: 9

Solution:

The multiples of 3 less than 30 are {3, 6, 9, 12, 15, 18, 21, 24, 27}, totaling 9 elements.

If set C = {x | x is a multiple of 3 and less than 30}, how many elements are in set C?

If set C = {x | x is a multiple of 3 and less than 30}, how many elements are in set C?

Step 1: Understand what a multiple of 3 is. A multiple of 3 is any number that can be divided by 3 without leaving a remainder.
Step 2: Identify the range we are interested in. We need multiples of 3 that are less than 30.
Step 3: Start listing the multiples of 3. Begin with 3 and keep adding 3 until you reach a number that is 30 or more.
Step 4: List the multiples: 3, 6, 9, 12, 15, 18, 21, 24, 27.
Step 5: Count the numbers in your list. There are 9 numbers: 3, 6, 9, 12, 15, 18, 21, 24, 27.
Step 6: Conclude that the total number of elements in set C is 9.

Set Theory – Understanding how to define and count elements in a set based on given criteria.
Multiples – Identifying multiples of a number and applying constraints such as being less than a certain value.
Inequalities – Applying the concept of inequalities to limit the range of numbers considered in a set.