ECM 1415 Set theory

Question 1

How to prove if a function is injective?

Answer 1

Assume f(x) = f(y) and show x = y

Question 2

How to prove if a function is surjective?

Answer 2

Consider an arbitrary element y such that B and x such that A so that f(x) = y

Question 3

How to prove if a function is not injective?

Answer 3

x, y such that A so that x/=y and f(x) = f(y)

Question 4

How to prove if a function is not surjective?

Answer 4

for all x such that A, find a y such that B that makes f(x) /= y

Question 5

What are the 3 properties of a function?

Answer 5

Injectivity
Surjectivity
Bijectivity

Question 6

how is the inverse function denoted?

Answer 6

f^-1(y) = x if f(x) = y

Question 7

What is injectivity

Answer 7

every element of the function’s codomain is the image of at most one element of its domain.

it is a one-to-one function

Every element of the codomain is either reach once or not at all

Question 8

What is surjectivity

Answer 8

every element of the function’s codomain is the image of at least one element of its domain.

It is an onto function

Every element of the codomain is reached at least once