CP 2 Sets and Functions 2 Flashcards
if A+B are sets a ____ from A to B is a subset of AxB if for every element in A there is exactly 1 element in B
Function
denoted f: A–>B
for a function (f:A–>B)
A is the __
and B is the ___
Domain (of f)
Codomain (of f)
what is another notation for (a,b) ∈ f
f(a) = b
TF a function is a set
T
if A={1,2,3} and B={15,20,25,30}
- which of the following are functions and why
- f:{(1,30),(1,25),(2,20)(3,15)}
- f:{(1,30),(3,15)}
-f:{(1,30),(2,20),(3,20)}
- f1 is not bc theres an element in A paired with multiple in B
- f2 is not a function bc theres 2 elements in Anot pointing to any in B
-f3 is a funcition bc f3⊆AxB
Injections are known as
one to one functions
what is a composition
if f:A–>B and g:B–>C
then the composition of fxg={(a,g(f(a))| a∈ A}
if f:A–>B and g:B–>A is _________
the inverse function
f=g^-1
TF for something to be a function, every element in A must be the preimage of something in B
T, A must have a matching B
TF something is not a function if 2 elements in A point to the same element in B
F, two elements of A can have the same image
TF a function is not an injection if there are leftover elements in B
F, it is still an injection if there is extra elements as long as every element in A is pointing at a unique image in B
TF a function is not an surjection if there are leftover elements in B
T, everything in B must be an image of something in A
what is a bijection
a function is both injective and surjective
what is another way of thinking about an ordered pair like (a,b)
like an arrow pointing from a to b
a———>b
TF in terms of a function, Multiple elements in 𝐴
can map to the same element in 𝐵, but no element in 𝐴 can map to more than one element in 𝐵
T
