How to find the dense subsets of a topological space

Question

I have the following problem and I'm having trouble putting the theory in practice.

Let $X = \{ a,b,c,d \}$ with the topology $T = \{\emptyset, \{a\}, \{b\}, \{a,b\}, X\}$. Find the subsets of $X$ that are dense in $X$.

Also, if you can help me with some theory for newbies in this subject, it would be awesome. :3

Answer 1

Take $A=\{a,b\}$. Then $A$ is dense in $X$ as any non empty open set intersects $A$. Also you can take another dense set say $\{a,b,c\}$...this is also a dense set since any non empty open set intersects it...In this way u can find out all the dense set in this space.