Mathematics Set Theory Quiz

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Questions and Answers

What is the roster form for the set of integers from -3 to 5?

  • {-2, -1, 0, 1, 2, 3, 4, 5}
  • {-3, -2, -1, 0, 1, 2, 3, 4}
  • {-3, -2, -1, 0, 1, 2, 3, 4, 5} (correct)
  • {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

Which of the following represents the set of all natural numbers which are multiples of 5 but less than 30 in set builder form?

  • {x | x > 0, x < 30, x mod 5 = 0}
  • {x | 0 < x < 30, x is a natural number, x = 5n for n ∈ N} (correct)
  • {x | x < 30, x is natural, x = 5n for n ∈ Z}
  • {x | x < 30, x is an integer, x mod 5 = 0}

How many students failed in either MATH or CS but not in both?

  • 10
  • 8 (correct)
  • 12
  • 5

Which of the following sets is a void set?

<p>{} (D)</p> Signup and view all the answers

What is the intersection of sets A and B, where A is the interval $(5, x)$ and $x < 8$?

<p>(5, 8) (B)</p> Signup and view all the answers

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Study Notes

Roster Form Sets

  • Set of integers from -3 to 5: {-3, -2, -1, 0, 1, 2, 3, 4, 5}
  • Set of natural numbers which are multiples of 5 and less than 30: {5, 10, 15, 20, 25}
  • Set of prime numbers between 10 and 40: {11, 13, 17, 19, 23, 29, 31, 37}

Set Builder Form Sets

  • Set {2, 4, 6, 8, 10, 12} in set builder form: {x | x is an even natural number, 2 ≤ x ≤ 12}
  • Set {5, 6, 7, 8, 9, 10} in set builder form: {x | 5 ≤ x ≤ 10}
  • Set {1, 4, 9, 16, 25} in set builder form: {x | x is a perfect square, x ≤ 25}

Types of Sets

  • Finite sets: Sets with a limited number of elements such as {2, 4, 6, 8, 10, 12}, {5, 6, 7, 8, 9, 10}, {1, 4, 9, 16, 25}
  • Infinite sets: Sets that go on indefinitely without end; specific examples not provided in the text
  • Void set: The empty set, containing no elements

Representing Letters in "College"

  • Set representing A: {A}
  • Set representing B: {B}
  • Set representing C: {C}
  • Set representing D: {D}

Set Operations on Intervals

  • Given A: {x | 5 < x < 8, x ∈ R} and B: {x | 1 < x < 8, x ∈ R}
  • Union of A and B (A ∪ B): {x | 1 < x < 8, x ∈ R}
  • Intersection of A and B (A ∩ B): {x | 5 < x < 8, x ∈ R}
  • Difference A - B: {x | 5 < x < 8, x ∈ R} excluding elements of B

Student Failures in Subjects

  • Total students: 20
  • Students failed in MATH: 10
  • Students failed in CS: 12
  • Students failed in both subjects: 7
  • Students failed in MATH only: 10 - 7 = 3
  • Students failed in CS only: 12 - 7 = 5
  • Students failed in either MATH or CS: (10 + 12 - 7) = 15
  • Students failed in either subject but not both: (3 + 5) = 8
  • Students who did not fail in any subject: 20 - 15 = 5

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