What is the conjunctive normal form of the boolean constant TRUE? I have the following problem: Is TRUE (or 1) a logically equivalent formel in conjuctive normal form to a tautology? How can I build the conjunctive normal form of TRUE if the output is always TRUE?

Here's a definition of a clause adapted from Merrie Bergmann's An Introduction to Many-Valued and Fuzzy Logic p. 20:

1. A literal (a letter or negation of a letter) is a clause.
2. If **P** and **Q** are clauses, then ( **P** ∨ **Q** ) is a clause.



Definition of conjunctive normal form.

1. Every clause is in conjunctive normal form.
2. If **P** and **Q** are in conjunctive normal form, then ( **P** ∧ **Q** ) is in conjunctive normal form.



So, "P" and "$\lnot$P" are both literals. Thus, by condition 2. of the definition of a clause, (P $\lor$ $\lnot$P) is a clause. So, by condition 1. of the definition of a clause, (P $\lor$ $\lnot$P) is in conjunctive normal form.

If ⊤ is a clause in your language, it also follows that ⊤ is in conjunctive normal form.