This can fit into the category of Hasty Generalization, this is, that you generalize with a lack of evidence or better,reasons as of to state that the trilogy of the Lord of The Rings isgood. It is good because it is good, if the first part is good, then all the trilogy is good.
Another option might be a fallacy called <em>ad populum </em> which takes place whenever you appeal to the public knowledge of something to prove it is true. In this case forexample, you could say: the reviews are giving this movie 5 stars, so this movie is good, because people like it.
Both sentences A and B are capitalized correctly:
Only one solution is possible: We must cut our expenses.
Only one solution is possible: we must cut our expenses.
The first word of both sentences (only) must always be capitalized since it is placed at the beginning.
On the other hand, if the sentence following the colon is dependent (it is incomplete), its first word should not be capitalized. For example:
"I have to buy three things: apples, oranges and bananas."
Regarding capitalization in independent clauses following a colon (such as the one given in the example), it is subject to the citation style the writer is following (APA, MLA, etc). While some styles recommend capitalization of the first word of the sentence, some others do not.
