Which relation from A={5,7} to B={1,2,3} is not a function?

Correct answer: {(5,1),(7,2),(7,3)}

For a relation from A to B to be a function, each element of the domain A must be associated with exactly one element of B. In option A, the input 5 maps to 1, but the input 7 maps to both 2 and 3. Since one input has two different images, this relation is not a function. In option B, both inputs have exactly one image, even though they share the same output 1; that is a valid many-one function. Options C and D also assign one output to each of 5 and 7. The key rule concerns repeated first components with different second components, not repeated second components. Therefore option A is the only correct answer.