Sets

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Questions and Answers

What is the name of the theorem that states that for any two sets, there exists a one-to-one correspondence between the set and its power set?

  • The Well-Ordering Principle
  • The Power Set theorem
  • Schroeder-Bernstein theorem
  • Cantor's diagonal argument (correct)

Which of the following is a property of an equivalence relation?

  • Irreflexivity, symmetry, and transitivity
  • Reflexivity, asymmetry, and transitivity
  • Reflexivity, symmetry, and transitivity (correct)
  • Irreflexivity, asymmetry, and transitivity

Which of the following is NOT an algebraic structure with one binary operation?

  • Fields
  • Monoids
  • Groups
  • Semi-groups

What is the well-ordering principle in mathematical induction?

<p>It states that every non-empty set of positive integers has a least element. (A)</p> Signup and view all the answers

Which of the following is true about bijective functions?

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What is the Division algorithm used for?

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What is the size of the power set of a set with n elements?

<p>2^n (D)</p> Signup and view all the answers

What is the power set theorem?

<p>It states that every set has a power set that is larger than the original set. (B)</p> Signup and view all the answers

What is the Power Set theorem?

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What is the difference between a monoid and a group?

<p>A group has inverses, but a monoid does not necessarily have them. (A)</p> Signup and view all the answers

What is the Euclidean algorithm used for?

<p>To find the greatest common divisor of two integers. (D)</p> Signup and view all the answers

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