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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram

Which one of the following sets is a null (empty) set?

The set of primes strictly between 8 and 10 is empty, because the only integer there is 9, which is composite. The set {0} contains the element zero, and x² = 4 has solutions 2 and −2.

  1. A{x : x is a natural number and x + 5 = 5}
  2. B{0}
  3. C{x : x is an integer and x² = 4}
  4. D{x : x is a prime number and 8 < x < 10}Correct

Explanation

Between 8 and 10 only 9 lies, and 9 is not prime, so that set is empty. {0} has one element. x + 5 = 5 gives x = 0, which is not a natural number in the usual convention, so that set is also empty. Check: that makes two empty sets, so the first option is flawed.

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