F2

Question 1

An area of mathematics that investigates sets and their properties, as well as operations on sets and cardinality, among many other topics. It is a fundamental subject of mathematics that serves as the foundation for many fields such as algebra, topology, and probability.

Answer 1

Set theory


Question 2

Used to describe the relationship between the elements of two sets. They are the mapping of elements from one set (the domain) to the elements of another set (the range), resulting in ordered pairs of the type (input, output).

Answer 2

Relations and functions

Question 3

Properties of Relations


Answer 3

Identity Relation
Empty Relation
Reflexive Relation
Irreflexive Relation
Inverse Relation
Symmetric Relation
Transitive Relation
Equivalence Relation
Universal Relation

Question 4

Each element only maps to itself in an ——–. Each element will only have one relationship with itself.

ex Id_A={(1,1),(2,2),(3,3)}

Answer 4

Identity Relation


Question 5

A relation where no element of a set is mapped to another set’s element or to itself.

ex. ∅_A={}

Answer 5

Empty Relation


Question 6

Every element in the relation maps back to itself.

Ex. R={(1,1),(2,2),(3,3),(1,2),(2,1)}

Answer 6

Reflexive Relation


Question 7

relation on a set where no element is related to itself.

Ex R={(1,2),(2,1),(2,3),(3,2)}

Answer 7

Irreflexive Relation


Question 8

he set of ordered pairs obtained by interchanging the first and second element in the ordered pair of a given relation.

R={(1,a),(2,b),(3,c),(2,a)}
R^-1={(a,1),(b,2),(c,3),(a,2)}

Answer 8

Inverse Relation


Question 9

The inverse relation might** not **always be a function if the original relation is a function

T or F

Answer 9

True

Question 10

is a type of binary relation on a set where if one element is related to another, then the second element is also related to the first in the same manner.

Answer 10

Symmetric Relation


Question 11

require that if the first element is connected to the second element and the second element is related to the third element, then the first element must also be related to the third element.

Answer 11

Transitive Relation

Question 12

is a fundamental concept in mathematics, particularly in areas such as set theory, abstract algebra, and topology.

Answer 12

Equivalence Relation


Question 13

It’s a relation that divides a set into disjoint subsets called

Answer 13

equivalence classes

Question 14

is one in which all of the elements from one set were related to all of the elements of some other set or to themselves.

Answer 14

Universal Relation


Question 15

can be used to describe languages (such as compiler grammar or a universal Turing computer). Graph traversal needs sets to keep track of node visits. Relational databases are completely based on set theory.

Answer 15

Sets and set relations