1. Preliminaries

Question 1

Map

Answer 1

A mapping from X to is a rule F that assigns to every element x∈X a unique element

Question 2

Domain of a Map

Answer 2

The X part of F:X->Y

Question 3

Target of a Map

Answer 3

The Y part of F:X->Y

Question 4

Composition of a Map

Answer 4

F:X->Y and G:W->X makes GoF:W->Y

Question 5

Binary Operation

Answer 5

Calculation involving 2 elements of a set to produce another element in the same set

Question 6

Closed under Binary Operation

Answer 6

Binary Operation works for every element in the set

Question 7

Inverse Image of a Map

Answer 7

Ex: if f(x)=x^2 then the inverse image of 4 is {-2,2}

Question 8

Injective Map

Answer 8

Every element of the domain maps to exactly 1 element in the codomain

Question 9

Surjective Map

Answer 9

Every element of the codomain maps to at least 1 element in the domain

Question 10

Bijective Map

Answer 10

Both Surjective & Injective

Question 11

Relation E on S

Answer 11

Let S be a nonempty set. A subset E of S × S is called a relation on S

Question 12

Equivalence Relation E on S

Answer 12

When the relation is reflexive, symmetric and transitive

Question 13

Equivalence Class

Answer 13

The set of all elements b ∈ S such that bEa

Question 14

Quotient of S by E (S/E)

Answer 14

The set of equivalence classes of an

equivalence relation E on S

Question 15

Representative of Equivalence Class

Answer 15

Element of an equivalence class

Question 16

Partition of S

Answer 16

A grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.

Question 17

3 Properties of a Partition

Answer 17

1. Doesnt contain empty set
2. Union of the sets equal to one big set X (said to cover X)
3. The intersection of 2 distinct set is empty.