9. TIle academic council at the U of A is seeking representation from among six students who are affiliated with four honor societies. The academic council representation includes three areas: mathematics, art, and engineering. At most two students in each area can be on the council. The following table shows the membership of the six students in the four honor societies:

Society 1

2 3

4 Affiliated students 1,2,3 1,3,5 3,4,5 1,2,4,6 The students who are skilled in the areas of mathematics, art, and engineering are shown in the following table:

272 Chapter 6 Network Models Area Skilled students Mathematics 1, 2, 4 Art 3,4 Engineering 4,5,6 A student who is skilled in more than one area must be assigned exclusively to one area only. Can all four honor societies be represented on the council?