Let $X$ be a topological space and let $A$ be a subset of $X$. Which of the
following statements are true?

a. If $A$ is dense in $X$, then $A^o$ (the interior of A), is also dense in $X$.

b. If $A$ is dense in $X$, then $X\setminus A$ is nowhere dense.

c. If $A$ is nowhere dense, then $X\setminus A$ is dense.

Attempt
a.False Try out $X=\mathbb{R}$ and $A=\mathbb{R}$

b,Flase Try out $X=\mathbb{R}$ and $A=\mathbb{Q}$

c.I Think its gonna be true because if $X=\mathbb{R}$ and $A=\mathbb{N}$ but hiw can I prove

P.S. I am new and poor in Latex. So forgive any mistakes commited.