The statement in the image says:

"A function is one-to-one if the set of ordered pairs are unique and distinct, that is there should be no repetition of $x$ and $y$ values."

This statement is False.

Explanation:

For a function to be one-to-one (or injective), each unique $x$-value must map to a unique $y$-value, meaning no two different $x$-values should map to the same $y$-value. However, the statement incorrectly suggests that there should be no repetition of both $x$ and $y$ values.

• Correct condition for one-to-one function: No two distinct $x$-values have the same $y$-value.
• Incorrect condition: No repetition of $x$ and $y$ values implies that both the domain and the range should be unique, which is not necessary for a function to be one-to-one.

Would you like more details or have any questions? Here are five related questions:

1. What is the definition of a bijective function?
2. How do you determine if a function is one-to-one using a graph?
3. Can a function be one-to-one but not onto? Explain.
4. What is the horizontal line test and how is it used?
5. How