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In a scenario where set B is defined as {x | x is a natural number and x < 10

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Question: In a scenario where set B is defined as {x | x is a natural number and x < 10}, which of the following elements would violate the constraints of set B?

Options:

  1. 5
  2. 10
  3. 0
  4. 7

Correct Answer: 10

Solution: 

The element 10 violates the constraint of being less than 10, thus it cannot be included in set B.

In a scenario where set B is defined as {x | x is a natural number and x < 10

Practice Questions

Q1
In a scenario where set B is defined as {x | x is a natural number and x < 10}, which of the following elements would violate the constraints of set B?
  1. 5
  2. 10
  3. 0
  4. 7

Questions & Step-by-Step Solutions

In a scenario where set B is defined as {x | x is a natural number and x < 10}, which of the following elements would violate the constraints of set B?
  • Step 1: Understand what set B is. Set B is defined as {x | x is a natural number and x < 10}. This means set B includes all natural numbers that are less than 10.
  • Step 2: Identify what natural numbers are. Natural numbers are the positive integers starting from 1, which are 1, 2, 3, 4, 5, 6, 7, 8, 9, and so on.
  • Step 3: List the natural numbers that are less than 10. These numbers are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
  • Step 4: Check the element in question, which is 10. We need to see if 10 is a natural number and if it is less than 10.
  • Step 5: Determine if 10 is a natural number. Yes, 10 is a natural number.
  • Step 6: Check if 10 is less than 10. No, 10 is not less than 10; it is equal to 10.
  • Step 7: Conclude that since 10 is not less than 10, it violates the constraints of set B and cannot be included in set B.
  • Set Theory – Understanding the definition and constraints of sets, particularly in relation to natural numbers.
  • Inequalities – Applying inequalities to determine membership in a set based on specified conditions.
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