23 Questions
What does the symbol | represent in set notation?
Such that
Which of the following represents a well-defined set?
{Odd numbers less than 10}
What is the correct form of the set using the listing method {2, 3, 2, 4, 3}?
{2, 3, 4}
Which of the following correctly represents a subset relationship?
{1, 2, 3} ⊆ {1, 3}
In set notation, what does Z+ represent?
Positive integers
How are elements represented in a set-builder notation?
{x | x is a prime number}
Which of the following sets is an equivalence class under the relation $R={(a,b)|a+b$ is even}?
{1,3,5}
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}}
In the context of equivalence relations, which pair of elements would be considered equivalent?
{apple, kiwi}
What is a key characteristic of a partial order among elements in a set?
Antisymmetric
Which set forms an equivalence class under the relation $R={(a,b)|a+b$ is even}?
{1,2,3}
What is a common characteristic of equivalence relations and partial orders?
Reflexive property
Which of the following best describes an anty symmetric relation?
No element precedes each other
In a reflexive relation defined on set {1,2,3,4,6}, which of the following statements is true?
$1$ divides $1$
For the relation $R={(a,b)| a$ divides by $b}$, which option represents an asymmetric relation?
$3$ divides $6$ but $6$ does not divide $3$
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 $1 ∈ 4$
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
What is the cardinality of set E = {x | x is odd, and x < 12}?
6
What is the cardinality of set A = {{1,2},{3,4,5},{6}}?
4
What is the cardinality of set A = {{1,2},{3,4,5},{∅},{6}}?
5
What is the cardinality of set A = {x | x is an even number, x > 10}?
0
What is the cardinality of set B = {x | x is an odd number, x < 5}?
1
What is the cardinality of set D = {1, 2, 3, 2, 1}?
3
Learn about sets in mathematics, where a set is a collection of objects called elements. Understand the concept of a well-defined set having no ambiguity about its elements. Explore examples like collections of red cars, positive numbers, people born before 1980, and different notations for sets.
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