Q:

What is the Conjunction Normal Form of a tautology?

I have a tautology and I need to write its CNF(Conjunction Normal Form). Since its a tautology CNF will not have any element. So should I write 1 in it or 0 ?

A:

Recall that $\varphi$ is in CNF if $\varphi = \varphi_1\land\cdots\land\varphi_k$ where $\varphi_i$ is a disjunction of atomic propositions and their negations.
Suppose $p$ is an atomic proposition (e.g. a propositional variable)
$$(p\lor\lnot p)$$

A:

CNF for a tautology presumably is a conjunction of no terms.  So just write $1$ for it.  Or $T$.  Depending on your notation.

