Takuzu (Binero) is a puzzle game

Takuzu (Binero) is a puzzle game, a distant cousin of Sudoku, in which you have to fill in a grid with 0s
or 1s while respecting the 3 following rules:

1. No more than two 0s or two 1s in a row or column
2. As many 0's as 1's in each row and in each column.
3. Not 2 identical rows or 2 identical columns.
   An example of an initial problem then solved
   1.1 Posing the problem
   Propose a way to describe the problem in terms of a set of
   variables describing a state, a starting state (values of the variables)
   variables), solution state (conditions on the values of the variables for a
   for a state to be a solution), possible actions/operators (with their conditions
   their conditions and their effect on the state description).
   1.2 Illustrate the first two levels of the solution tree
   according to your model.
   Be careful to keep only the possible operations to present the
   2 levels and limit to 3 operations described per level.
   1.3 Recall what a heuristic is and which heuristic could be used for example for this problem
   Put the following expressions in disjunctive normal form
   using implication, equivalence and De Morgan's laws.
   a. P → ((Q ∧ R) → S
   b. ((¬P ∧ Q) → S)