“Nucleotides are the building blocks of nucleic acids; they are composed of three subunit molecules: a nitrogenous base (also known as nucleobase), a five-carbon sugar (ribose or deoxyribose), and at least one phosphate group.”
Cytosine is not a nucleotide, it is a base from which a nucleotide can be formed.
Cytidine is a nucleoside, i.e. a base plus ribose.
Cytidine monophosphate is a nucleotide, because it contains a base, a sugar and a phosphate group. Cytidine monophosphate is one of the nucleotides used in RNA.
Cyclic cytidine monophosphate is also a nucleotide. It is what you get if you break up RNA on the other side of the phosphate link, so that the phosphate group is attached to the 3’ carbon atom of the downstream ribose component rather than the 5’ carbon atom of the upstream ribose group. Molecules of cyclic cytidine monophosphate can combine to form RNA chains as shown below. Thus, while cyclic cytidine monophosphate is not the nucleotide which is usually involved in the formation of RNA, it is still an RNA nucleotide.
So cytosine is not an RNA nucleotide, but cyclic cytidine monophosphate is. The slide is correct, and you are completely wrong.
(Drat! Ninjaed by Rumraket!)