Discrete Structures Week 7 Flashcards
map/function
V- x C- A, E a unique y C- B such that f(x) = y
domain and codomain
domain -> codomain
cartesian product
sets A and B
A x B = { (a,b) | a C- A, b C- B}
A^2
if A=B then A x B = A^2
A^3
A^2 x A
= { (a,b,c) | a,b,c C- A}
A^n
= {a1,a2,…,an | ai C- A for V- i}
graph of function
= { (x,f(x)) | x C- A}
A x B = B x A ?
no
example on notes
not in the image means
no preimage
no preimage means
not in image
image
= { f(x) | x C- A } c_ B
preimage/inverse image
f ^-1 (y) = { x | f(x) = y }
identity map
f : Z -> Z
x |-> x
know how to graph a function and come up with its set notation
:)
continuous vs just dots
depends on the domain and codomain
injection
f: A->B is an injection
if V-x1,x2 C- A such that X1!=X2
then f(x1)!=f(x2)
by contrapositive…
-2 different elements have 2 different outputs
-a preimage only has one element
subjection
f:A->B is surjection
if f(A) = B
image = codomain
V-y C- B, Ex C- A such that f(x) = y
-all elements in codomain are hit
-every element in codomain B needs a preimage
