Functions

Question 1

partial function

Answer 1

a function that is defined on a subset of a set, rather than the entire set

Question 2

total function

Answer 2

a function defined for every element of the domain

Question 3

surjective functions are also known as

Answer 3

onto functions

Question 4

surjective functions have a range equal to…

Answer 4

their codomain

Question 5

example of a violation of a property of surjective functions

Answer 5

there is some element of the codomain of set A, which does not map onto an input value.

Question 6

example of a violation of a property of total functions

Answer 6

there is some value in the set that has an undefined output

Question 7

total functions refer to the completeness of the _______ while partial functions refer to the completeness of the ________

Answer 7

domain, codomain

Question 8

how to prove injectivity

Answer 8

confirm it is a total function and show that the function and its inverse are mutually inverse

Question 9

how to prove bijectivity

Answer 9

confirm it is total, then confirm it is has an inverse which is also total

Question 10

a bijection is injective in

Answer 10

both directions