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

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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?

{1, 2, 3} ⊆ {1, 3} Signup and view all the answers

In set notation, what does Z+ represent?

Positive integers Signup and view all the answers

How are elements represented in a set-builder notation?

{x | x is a prime number} 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}?

{1,3,5} 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}?

{{1,2},{3,4},{5,6}} Signup and view all the answers

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

{apple, kiwi} Signup and view all the answers

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

Antisymmetric Signup and view all the answers

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

{1,2,3} Signup and view all the answers

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

Reflexive property Signup and view all the answers

Which of the following best describes an anty symmetric relation?

No element precedes each other 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?

$1$ divides $1$ Signup and view all the answers

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

$3$ divides $6$ but $6$ does not divide $3$ 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?

$1 ∈ 2$ and $2 ∈ 4$ implies $1 ∈ 4$ 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?

Incomparable Signup and view all the answers

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

6 Signup and view all the answers

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

4 Signup and view all the answers

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

5 Signup and view all the answers

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

0 Signup and view all the answers

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

1 Signup and view all the answers

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

3 Signup and view all the answers