Set Theory
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Questions and Answers

If A and B are two sets, then what is A – B equal to?

  • A ∪ B
  • A ∪ B'
  • A ∩ B
  • A ∩ B' (correct)

    • For any set A, what is the result of A ∪ A?

  • A (correct)
  • U
  • A ∩ A
  • A ∪ ∅

    • Which of the following is true according to De Morgan's law?

  • (A ∩ B)' = A' ∪ B'
  • (A ∪ B)' = A' ∪ B'
  • (A ∪ B)' = A' ∩ B' (correct)
  • (A ∩ B)' = A' ∪ B'

    • What is the result of A ∩ U for any set A?

    <p>A</p> Signup and view all the answers

    If A, B and C are three sets, then A × (B ∪ C) is equal to?

    <p>(A × B) ∪ (A × C)</p> Signup and view all the answers

    If A and B are two sets, what is the result of A Δ B?

    <p>B Δ A</p> Signup and view all the answers

    What is the result of A ∩ (B ∪ C) for any three sets A, B, and C?

    <p>(A ∪ B) ∩ C</p> Signup and view all the answers

    What is A ∩ (B – C) equal to?

    <p>(A ∩ B) – (A ∩ C)</p> Signup and view all the answers

    If A, B and C are three sets, then (A – B) ∪ (B – A) is equal to?

    <p>(A ∪ B) – (A ∩ B)</p> Signup and view all the answers

    What is the result of A - (B - C) for any three sets A, B, and C?

    <p>(A - C) - B</p> Signup and view all the answers

    If A and B are two sets, then what is A – B equal to?

    <p>A ∩ Bc</p> Signup and view all the answers

    If A, B, and C are any three sets, then A – (B ∪ C) is equal to?

    <p>(A – B) ∩ (A – C)</p> Signup and view all the answers

    If A and B are two non-empty sets, then what is (A – B) ∪ (B – A) equal to?

    <p>(A ∪ B) – (A ∩ B)</p> Signup and view all the answers

    Let A and B be two non-empty sets. What is A × B equal to?

    <p>{(a, b) : a ∈ A and b ∈ B}</p> Signup and view all the answers

    If A and B are two non-empty sets, then what is A – (A ∩ B) equal to?

    <p>A – B</p> Signup and view all the answers

    Which of the following sets is a null set?

    <p>The set {x : x^2 + 1 = 0 and x is real}</p> Signup and view all the answers

    If A is a set of integers, what is the set notation for A?

    <p>A = {x | x is an integer and x = 2n for n ∈ Z}</p> Signup and view all the answers

    What is the set notation for the set of all even natural numbers?

    <p>E = {x | x is a natural number and x = 2n for n ∈ N}</p> Signup and view all the answers

    Which of the following is a well-defined collection?

    <p>The set of all students in a class</p> Signup and view all the answers

    What is the set of all real numbers denoted by?

    <p>R</p> Signup and view all the answers

    What is a common term used to describe the objects that constitute a set?

    <p>Elements</p> Signup and view all the answers

    What is the purpose of a rule in defining a set?

    <p>To tell whether a given object belongs or does not belong to the set</p> Signup and view all the answers

    What is the significance of the order in which elements are written in a set?

    <p>It makes no difference</p> Signup and view all the answers

    What is the symbol used to read as 'such that' in the set-builder method?

    <p>|</p> Signup and view all the answers

    What is the notation used to describe a set using the roster method?

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

    What is the total number of subsets of a set A with n elements?

    <p>$2^n$</p> Signup and view all the answers

    If a set A has $m$ elements and a set B has $n$ elements, and the total number of subsets of A is 56 more than the total number of subsets of B, what are the values of $m$ and $n$?

    <p>m = 6, n = 3</p> Signup and view all the answers

    What is the number of proper subsets of the set {1, 2, 3}?

    <p>6</p> Signup and view all the answers

    If X = {8n - 7n - 1 : n ∈ N} and Y = {49(n - 1) : n ∈ N}, then what is the relationship between X and Y?

    <p>X ⊆ Y</p> Signup and view all the answers

    If A = {x : x ∈ R, x^2 = 16 and 2x = 6}, what is the value of A?

    <p>∅</p> Signup and view all the answers

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