If a constraint-based set is defined as {x | x is a multiple of 3 and x < 30}

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Question: If a constraint-based set is defined as {x | x is a multiple of 3 and x < 30}, how many elements does this set contain?

Options:

Correct Answer: 10

Solution:

The multiples of 3 less than 30 are 3, 6, 9, 12, 15, 18, 21, 24, 27, totaling 10 elements.

If a constraint-based set is defined as {x | x is a multiple of 3 and x < 30}, how many elements does this set contain?

If a constraint-based set is defined as {x | x is a multiple of 3 and x < 30}, how many elements does this set contain?

Step 1: Understand the constraint-based set definition. It says we need numbers that are multiples of 3 and also less than 30.
Step 2: Identify the multiples of 3. These are numbers you get when you multiply 3 by whole numbers (0, 1, 2, 3, ...).
Step 3: List the multiples of 3: 3 * 1 = 3, 3 * 2 = 6, 3 * 3 = 9, 3 * 4 = 12, 3 * 5 = 15, 3 * 6 = 18, 3 * 7 = 21, 3 * 8 = 24, 3 * 9 = 27.
Step 4: Check if these multiples are less than 30. All the numbers listed (3, 6, 9, 12, 15, 18, 21, 24, 27) are less than 30.
Step 5: Count the numbers in the list. There are 9 numbers: 3, 6, 9, 12, 15, 18, 21, 24, 27.
Step 6: Conclude that the set contains 9 elements.

Set Theory – Understanding how to define and count elements in a set based on given constraints.
Multiples and Divisibility – Identifying multiples of a number and applying constraints to find valid elements.
Inequalities – Applying the concept of inequalities to limit the range of values in a set.