Question

Function f from A to B is called onto, or a surjection, if and only if for some element b ∈ B there is an element a ∈ A with f (a) = b.

true or false

Answer 1

A function is onto, or a surjection, if every element in the codomain is mapped to by at least one element in the domain.

Step-by-step explanation:

A function from set A to set B is called onto, or a surjection, if and only if for some element b in set B there is an element a in set A with f(a) = b.

In simpler terms, a function is onto if every element in the codomain B is mapped to by at least one element in the domain A.

For example, let's consider a function f from set A = {1, 2, 3} to set B = {4, 5}.
f = {(1, 4), (2, 4), (3, 5)}
In this case, the function is onto because every element in set B is mapped to by at least one element in set A. Both elements 4 and 5 have corresponding elements in set A.