Which relation from A = {a,b,c} to B = {1,2} is not a function?

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

The governing rule is that every element of the domain must have exactly one image in the codomain. In option A, a and b each have one image, but c is paired with both 1 and 2. Thus the same input c has two different outputs, which violates the definition of a function. Options B, C, and D each contain exactly one pair beginning with a, one beginning with b, and one beginning with c, so each can represent a function from A to B. It is permissible for different inputs to share an output, as seen in option C; the restriction concerns one input having multiple outputs. Therefore option A is the only non-function.