What is the definition of when each input has exactly one output in a relation

The word you’re looking for is a *function*. Functions can’t have one input associated with more than one output, but multiple inputs *can* produce the same output (so-called “even functions” have this property), and the special functions where each output has exactly one input associated with it are called “one-to-one” functions.

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.