Which of the following relations, defined on the domain \({1,2,3}\), is a function but not a one-one function?

Correct answer: {(1,a),(2,a),(3,c)}

In option A, each domain element 1, 2, and 3 has exactly one image, so it is a function. However, 1 and 2 both have the image a; hence different inputs have the same output, so the function is not one-one. Option C is one-one, whereas B and D assign two images to the same input and therefore are not functions. Exam tip: for a function, every input must have exactly one output; for a one-one function, distinct inputs must also have distinct outputs.