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}, which of the following is NOT an element of this set?

Options:

Correct Answer: 31

Solution:

The number 31 is not an element of the set as it does not meet the constraints of being a multiple of 3 and less than 30.

If a constraint-based set is defined as {x | x is a multiple of 3 and x < 30}, which of the following is NOT an element of this set?

If a constraint-based set is defined as {x | x is a multiple of 3 and x < 30}, which of the following is NOT an element of this set?

Step 1: Understand the set definition. The set is defined as {x | x is a multiple of 3 and x < 30}. This means we are looking for numbers that are both multiples of 3 and less than 30.
Step 2: Identify the multiples of 3 that are less than 30. These numbers are: 0, 3, 6, 9, 12, 15, 18, 21, 24, 27.
Step 3: Check the number 31. We need to see if 31 is a multiple of 3 and if it is less than 30.
Step 4: Determine if 31 is a multiple of 3. 31 divided by 3 equals approximately 10.33, which is not a whole number, so 31 is not a multiple of 3.
Step 5: Check if 31 is less than 30. 31 is greater than 30, so it does not meet the second condition either.
Step 6: Conclude that since 31 does not meet either condition (not a multiple of 3 and not less than 30), it is NOT an element of the set.

Set Theory – Understanding the definition and elements of a set based on given constraints.
Multiples – Identifying multiples of a number (in this case, 3) within a specified range.
Inequalities – Applying the concept of inequalities to determine if a number meets the condition of being less than a specified value (30).