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In a scenario where a set is defined by the constraints 'x is a positive integer

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Question: In a scenario where a set is defined by the constraints \'x is a positive integer and x is less than or equal to 20\', which of the following statements is true?

Options:

  1. The set includes negative integers.
  2. The set includes the number 20.
  3. The set includes zero.
  4. The set includes fractions.

Correct Answer: The set includes the number 20.

Solution: 

The set includes the number 20 as it satisfies the constraint of being a positive integer less than or equal to 20.

In a scenario where a set is defined by the constraints 'x is a positive integer

Practice Questions

Q1
In a scenario where a set is defined by the constraints 'x is a positive integer and x is less than or equal to 20', which of the following statements is true?
  1. The set includes negative integers.
  2. The set includes the number 20.
  3. The set includes zero.
  4. The set includes fractions.

Questions & Step-by-Step Solutions

In a scenario where a set is defined by the constraints 'x is a positive integer and x is less than or equal to 20', which of the following statements is true?
  • Step 1: Understand the constraints given in the question. The constraints are that 'x is a positive integer' and 'x is less than or equal to 20'.
  • Step 2: Identify what a positive integer is. Positive integers are whole numbers greater than zero, such as 1, 2, 3, and so on.
  • Step 3: Determine the range of positive integers that are less than or equal to 20. This includes all numbers from 1 to 20.
  • Step 4: Check if the number 20 fits within the defined set. Since 20 is a positive integer and it is equal to 20, it satisfies both constraints.
  • Step 5: Conclude that the statement about the number 20 being included in the set is true.
  • Set Definition – Understanding how to define a set based on given constraints, specifically focusing on positive integers and their limits.
  • Inequalities – Interpreting inequalities correctly, particularly the meaning of 'less than or equal to' in the context of set membership.
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