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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?

It states that every non-empty set of positive integers has a least element. 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?

2^n Signup and view all the answers

What is the power set theorem?

It states that every set has a power set that is larger than the original set. 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?

A group has inverses, but a monoid does not necessarily have them. Signup and view all the answers

What is the Euclidean algorithm used for?

To find the greatest common divisor of two integers. Signup and view all the answers

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Description

Sharpen your understanding of Sets, Relations, and Functions with this comprehensive quiz. Test your knowledge on fundamental concepts such as Laws of Sets, Binary Relations, Equivalence Relations, and more. Explore the intricacies of functions, including bijective functions, inverse and composite functions, and the size of a set. Challenge yourself with complex topics such as Cantor's diagonal argument and the Power Set theorem. Perfect for students and enthusiasts alike, this quiz is a must-try for anyone seeking to master Sets