Question

\(f:X \to Y\) will be an onto function if and only if its range is

• A. \(X\)
• B. \(X\cap Y\)
• C. \(Y\)
• D. \(X\cup Y\)

Hint:

Onto means every element of the codomain is hit — range equals the codomain.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
By definition, a function \(f:X\to Y\) is onto (surjective) when every element of the codomain \(Y\) is the image of at least one element of \(X\).

Step 2: Applying the definition:
This is exactly the statement that the range of \(f\) (the set of all actual outputs) equals the whole codomain \(Y\), not just a subset of it.

Final Answer:
An onto function must have range \(=Y\).\[ \boxed{Y} \]