Discussion
Let \(X = \{a, b, c, d, e, f\}\) and \(Y = \{7, 8, 9, 10, 11\}\) be two sets. Which one of the following is true?
Answer: E
The true statement is one-to-one function cannot be defined from \(X\) to \(Y\).
\(X\) has 6 elements and \(Y\) has 5. A one-to-one function must send the 6 elements of \(X\) to 6 different elements of \(Y\), which is impossible (pigeonhole principle).
The sets in the first and third options leave \(f\) without an image, so they are not functions from \(X\) at all. The second sends both \(b\) and \(f\) to 11, so it is not one-to-one. The fourth sends both \(c\) and \(f\) to 9, so it is not one-to-one either.
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