Al Ansar University Maiduguri CSC 203: Set Theory in Discrete Data Structures
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Questions and Answers

What does the symbol | represent in set notation?

  • Not a member of
  • Greater than
  • Such that (correct)
  • Is equal to

Which of the following represents a well-defined set?

  • {All the cars in the world}
  • {All big things}
  • {Blue, Red, Beautiful}
  • {Odd numbers less than 10} (correct)

What is the correct form of the set using the listing method {2, 3, 2, 4, 3}?

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

Which of the following correctly represents a subset relationship?

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

In set notation, what does Z+ represent?

<p>Positive integers (A)</p> Signup and view all the answers

How are elements represented in a set-builder notation?

<p>{x | x is a prime number} (A)</p> Signup and view all the answers

Which of the following sets is an equivalence class under the relation $R={(a,b)|a+b$ is even}?

<p>{1,3,5} (C)</p> Signup and view all the answers

What is a partition of set $S={1,2,3,4,5,6}$ with respect to the relation $R={(a,b)|a+b$ is even}?

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

In the context of equivalence relations, which pair of elements would be considered equivalent?

<p>{apple, kiwi} (A)</p> Signup and view all the answers

What is a key characteristic of a partial order among elements in a set?

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

Which set forms an equivalence class under the relation $R={(a,b)|a+b$ is even}?

<p>{1,2,3} (C)</p> Signup and view all the answers

What is a common characteristic of equivalence relations and partial orders?

<p>Reflexive property (A)</p> Signup and view all the answers

Which of the following best describes an anty symmetric relation?

<p>No element precedes each other (C)</p> Signup and view all the answers

In a reflexive relation defined on set {1,2,3,4,6}, which of the following statements is true?

<p>$1$ divides $1$ (C)</p> Signup and view all the answers

For the relation $R={(a,b)| a$ divides by $b}$, which option represents an asymmetric relation?

<p>$3$ divides $6$ but $6$ does not divide $3$ (D)</p> Signup and view all the answers

In the power set of set $S={1,2,4}$, if the relation $R={(a,b)| a∈b}$ is defined, which of the following is true about the transitive property?

<p>$1 ∈ 2$ and $2 ∈ 4$ implies $1 ∈ 4$ (A)</p> Signup and view all the answers

Establishing an order among fruits based on size, if banana is less than orange but grape & kiwi are incomparable, what type of relation exists between grape and kiwi?

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

What is the cardinality of set E = {x | x is odd, and x < 12}?

<p>6 (C)</p> Signup and view all the answers

What is the cardinality of set A = {{1,2},{3,4,5},{6}}?

<p>4 (A)</p> Signup and view all the answers

What is the cardinality of set A = {{1,2},{3,4,5},{∅},{6}}?

<p>5 (D)</p> Signup and view all the answers

What is the cardinality of set A = {x | x is an even number, x > 10}?

<p>0 (B)</p> Signup and view all the answers

What is the cardinality of set B = {x | x is an odd number, x < 5}?

<p>1 (A)</p> Signup and view all the answers

What is the cardinality of set D = {1, 2, 3, 2, 1}?

<p>3 (B)</p> Signup and view all the answers

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