Math Problem Statement

Which is TRUE about onto function? 1. Every element in the co-domain must have an arrow pointing to it from some element of the domain. 2. Every element in the domain must have an arrow pointing to it from some element of the co-domain. Options: A. I only B. II only C. I and II D. neither I nor II

Solution

The problem concerns the definition of an onto function (also known as a surjective function). Let's analyze the statements:

  1. Every element in the co-domain must have an arrow pointing to it from some element of the domain.
    This is correct. An onto function ensures that every element of the co-domain is mapped to by at least one element of the domain. This is a defining property of surjective functions.

  2. Every element in the domain must have an arrow pointing to it from some element of the co-domain.
    This statement is incorrect. This would describe an injective or one-to-one relationship in the reverse sense, which is not relevant for surjectivity.

Thus, the correct answer is A. I only.

Would you like further clarification? Here are some related questions for practice:

  1. What is the definition of an injective function?
  2. How does a bijective function differ from an onto function?
  3. Can a function be both injective and surjective? If so, what is it called?
  4. What are some real-life examples of surjective functions?
  5. How can you verify if a function is surjective given its formula?

Tip: To check if a function is onto, ensure that every value in the co-domain is reachable by some input in the domain.

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Math Problem Analysis

Mathematical Concepts

Functions
Onto Functions
Surjective Functions

Formulas

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Theorems

Definition of Surjective (Onto) Functions

Suitable Grade Level

Grades 9-12