I recently came across this question as a part of exercise problems without answers and cannot figure it out. I know how to show that it is not surjective but have no idea how to do it for injectivity. I don't need a full answer a hint would be just fine. Thanks.
In order for the function to be injective, for every element of the domain (in this case B) there must be a distinct element of the codomain (in this case C) that it maps to. As the domain is larger than the codomain this means that there must be more than one element of the domain mapped to a single element of the codomain thus it is not injective.
This is what I have come up with but not sure if it is correct or even a step in the right direction.