Set Theory Basics: Empty Set and Universe

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Questions and Answers

If x ∈ C, what does that imply according to the text?

  • x is in set A only
  • x is not in set A or B
  • x is in set B only
  • x is in set A and B (correct)

What does it mean when two sets A and B are disjoint?

  • A ∩ B is the empty set (correct)
  • A and B are subsets of each other
  • A and B have elements in common
  • A ∪ B includes all elements of A and B

If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?

  • {2, 3} (correct)
  • {2, 3, 4}
  • {}
  • {1, 2, 3, 4}

In the context of sets, what does x ∈ C mean?

<p>x is an element common to A and B (D)</p> Signup and view all the answers

If A = {1, 2, 3} and B = {4, 5, 6}, what is A ∪ B?

<p>{1, 2, 3, 4, 5, 6} (A)</p> Signup and view all the answers

Which of the following best defines a set?

<p>A collection of elements (C)</p> Signup and view all the answers

If set A = {1, 2, 3}, what type of set is A?

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

What kind of function is used to show that a set is countable?

<p>One-to-one and onto function (A)</p> Signup and view all the answers

If set A = {0, 2, 4, 6, 8, ...}, what term best describes it?

<p>Countable (B)</p> Signup and view all the answers

What is the universal set in set theory notation often represented as?

<p>[0, 1] (A)</p> Signup and view all the answers

Which term describes a set that contains no elements?

<p>Empty set (D)</p> Signup and view all the answers

In set theory, what does the symbol ϕ represent?

<p>The empty set (D)</p> Signup and view all the answers

If A = {1, 2, 3, 4, 5, 6, 7, 8}, which of the following is true?

<p>{1, 2, 3} is a subset of A (D)</p> Signup and view all the answers

What does it mean if a set A is said to be not equal to {1, 2, 3}?

<p>Set A contains elements other than {1, 2, 3} (D)</p> Signup and view all the answers

Which of the following statements about the union of sets A and B is correct?

<p>(A ∪ B) contains elements exclusive to either set A or set B (B)</p> Signup and view all the answers

If a ∈ B implies a ∈ A, what can we conclude?

<p>Set B is a subset of set A (C)</p> Signup and view all the answers

What does x ∈ C represent in the context of set theory?

<p>{x} is an element of set C (A)</p> Signup and view all the answers

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