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If a constraint-based set is defined as 'the set of all x such that x is a multi

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Question: If a constraint-based set is defined as \'the set of all x such that x is a multiple of 3 and x < 30\', which of the following is an element of this set?

Options:

  1. 27
  2. 29
  3. 31
  4. 15

Correct Answer: 27

Solution: 

27 is a multiple of 3 and is less than 30, making it an element of the set.

If a constraint-based set is defined as 'the set of all x such that x is a multi

Practice Questions

Q1
If a constraint-based set is defined as 'the set of all x such that x is a multiple of 3 and x < 30', which of the following is an element of this set?
  1. 27
  2. 29
  3. 31
  4. 15

Questions & Step-by-Step Solutions

If a constraint-based set is defined as 'the set of all x such that x is a multiple of 3 and x < 30', which of the following is an element of this set?
  • Step 1: Understand the constraint-based set definition. It includes all numbers (x) that are multiples of 3 and also less than 30.
  • Step 2: Identify what a multiple of 3 is. A multiple of 3 is any number that can be divided by 3 without leaving a remainder (e.g., 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...).
  • Step 3: List the multiples of 3 that are less than 30. These are: 3, 6, 9, 12, 15, 18, 21, 24, 27.
  • Step 4: Check if 27 is in the list of multiples of 3 that are less than 30. It is included.
  • Step 5: Conclude that since 27 is a multiple of 3 and is less than 30, it is an element of the set.
  • Multiples of a Number – Understanding what it means for a number to be a multiple of another number, specifically multiples of 3.
  • Inequalities – Interpreting and applying the condition that a number must be less than 30.
  • Set Definition – Understanding how to define and identify elements of a set based on given constraints.
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