Axiom A There exists at least 1 tree Axiom B Every row has e

Axiom A: There exists at least 1 tree. Axiom B: Every row has exactly 2 trees. Axiom C: Every tree belongs to at least 1 row. Axiom D: Any 2 trees have exactly 1 row in common. Axiom E: For every row R there is exactly 1 other row having no trees in common with R.

Solution

Let us denote the 6 committees as C₁, C₂, C₃, C₄, C₅ and C₆

To assign the 4 persons – Akin, Berg, Chen and Diaz to 6 committees

Let us denote the persons as A, B, C and D respectively.

So the problem reduced to assigning 4 persons A, B, C and D to 6 committees C₁, C₂, C₃, C₄, C₅ and C₆ such that

Therefore the distribution will be as shown below:

C₁ A, B

C₂ A, C

C₃ A, D

C₄ B, C

C₅ B, D

C₆ C, D

Each committee has 2 persons.

4 persons distributed to 6 committees as ⁴C₂ = 6