I found this in my notes. I’m sure the idea isn’t mine, but my notes don’t indicate where I got the idea from or if this a quotation or merely a paraphrase.
If an act A is forbidden, then doing A is bad and not doing A is good.
If an act A is obligatory, then doing A is good and not doing A is bad.
This seems right to me. Notice, however, that doing an act can be good but not obligatory. In such a case, we would call the act supererogatory. So A’s goodness is a necessary but not a sufficient condition for A’s being obligatory. Likewise, A’s badness is a necessary but not a sufficient condition for A’s being forbidden.
So what are the sufficient conditions for A’s being forbidden, obligatory, or merely permitted? The answer is, “It depends.” It depends on one’s theory of moral ontology. For example, a Divine Command Theorist (DCTist) would say, “God’s commanding us to do A is a necessary and sufficient condition for being obligatory” and “God’s commanding us not to do A is a necessary and sufficient condition for being forbidden.”