Discrete Structures Week 6

Question 1

function/map

Answer 1

let A and B be two non-empty sets.
A function/map from A to B is an assignment that to every x C- A, assign a unique y C- B.

f: A -> B
x |-> f(x) = y C- B

Question 2

Image

Answer 2

image of A = range of f
ex in notes

Question 3

inverse image

Answer 3

of y is x
ex in notes

Question 4

equal functions

Answer 4

two functions
f : A -> B
g: A -> B
are equal if
f(x) = g(x), V-x C- A

Question 5

identity map

Answer 5

id sub A : A -> A
x |-> x

Question 6

restriction

Answer 6

f : A -> B
c c_ A
restriction of f to c is

f | sub c : c -> B
x |-> f (x)

image and pre-image changes

Question 7

cartesian product

Answer 7

of 2 sets A and B denoted by A x B is the set whose elements are points (x,y) whe x C- A and y C- B

A x B = { (x,y) | x C- A, y C- B}

Question 8

A x A n times

Answer 8

A ^ n = (x1, x2, …xn) | each x C- A}

Question 9

graph of a funtion

Answer 9

a function f : A-> B define a subset of A x B

graph of f: { (x,y) C- A x B | y = f(x)}

= { (x,f(x)) C- A x B | x C- A}