Chapter 5 definitions

Question 1

Define a function/mapping:

Answer 1

Let A and B be non empty sets. α: A->B is a function or mapping if it is a rule that assigns each element of A with exactly one element of B.

Question 2

Define the domain of α

Answer 2

Let α: A->B. A is called the domain of α denoted by D(α)

Question 3

Define the codomain of α

Answer 3

Let α: A->B. B is called to codomain of α denoted by CoD( α )

Question 4

define the range of α

Answer 4

α(A) = { α(a) | a ∈ A} is called the range or image of α denoted by Im(α)

Question 5

Define the graph of α

Answer 5

graph of α, G(α) = {(a,α(a)) | a ∈ A}

Question 6

Define a binary operation

Answer 6

If A = S x S, B = S then a mapping

Question 7

Define an identity mapping

Answer 7

α : A → B, A ⊆ B is called an identity mapping on A if α(a) = a ∀a ∈ A (denoted by α = 1 sub A)

Question 8

Define injective

Answer 8

α : A → B is one to one or injective, if α(a1) = α(a2) ⇒ a1 = a2 ∀a1, a2 ∈ A

Question 9

Define surjective

Answer 9

α : A → B is onto (surjective) if
∀ b ∈ B ∃a ∈ A | b = α(a)

Question 10

Define a bijection

Answer 10

If