Which of the following statements are true?

$(i)$ Every logic network is equivalent to one using just NAND gates or just NOR gates.
$(ii)$ Boolean expressions and logic networks correspond to labelled acyclic digraphs.
$(iii)$ No two Boolean algebras with $n$ atoms are isomorphic.
$(iv)$ Non-zero elements of finite Boolean algebras are not uniquely expressible as joins of atoms.

Choose the correct answer from the code given below:

Statement $(i)$ is true.

NAND and NOR gates are functionally complete gates.

So, every logic network can be represented using only NAND gates or only NOR gates.

Statement $(ii)$ is true.

Boolean expressions and logic networks can be represented using labelled acyclic digraphs.

Statement $(iii)$ is false.

Any two Boolean algebras with the same number of atoms are isomorphic.

Statement $(iv)$ is false.

In a finite Boolean algebra, every non-zero element can be uniquely expressed as a join of atoms.

Therefore, only $(i)$ and $(ii)$ are true.