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: Eliminating wrong options:
Range \(X\) or \(X\cap Y\) make no sense since range is a subset of the codomain \(Y\), not the domain \(X\). Range \(X\cup Y\) is also impossible since range \(\subseteq Y\) always.

Step 2: Confirming by elimination:
Only range \(=Y\) is consistent with range being a subset of \(Y\) that covers all of \(Y\).

Final Answer:
\[ \boxed{Y} \]