Question

In Discrete Structures, we learn about One to One Onto Functions. In 2 - 3 complete paragraphs (4 to 5 sentences each), include in your summary: What are One to One Onto Functions? Define and explain the terms injective, surjective, and bijective. Give examples.

Note: Each paragraph should contain 4-5 complete sentences and have no grammar/spelling errors.

Answer 1

One-to-one onto functions, or bijective functions, are functions that are both injective and surjective. Injective functions map different elements from the domain to different elements in the codomain, while surjective functions map every element in the codomain to at least one element in the domain.

Step-by-step explanation:

In Discrete Structures, one-to-one onto functions are functions that are both injective and surjective. An injective function, also known as a one-to-one function, maps different elements from the domain to different elements in the codomain.

This means that no two distinct elements in the domain are mapped to the same element in the codomain. For example, the function f(x) = x^2 is not injective because different values of x can result in the same value of f(x).

A surjective function, also known as an onto function, maps every element in the codomain to at least one element in the domain. This means that every element in the codomain has a preimage in the domain. For example, the function g(x) = 2x is surjective because every real number can be obtained by multiplying some number by 2.

A function that is both injective and surjective is called a bijective function. For example, the function h(x) = x is a bijective function because it maps every element to itself in a one-to-one correspondence.