Set Notation/Theory help

1. The problem statement, all variables and given/known data



Three tests are available to identify six different substances.



Test 1 is true in the presence of substance 1,2,3, and 4

Test 2 is true in the presence of substance 3,4, and 5

Test 3 is true in the presence of substance 2,5, and 6



Using set notation to denote the events that a substance under test is



a) substance 1

b) substance 2

c) substance 6



2. Relevant equations



Let [itex]E_{i}[/itex] denote the event that the i'th test is positive, [itex]i= 1, 2, 3[/itex]



3. The attempt at a solution



How do I properly represent the answers in set notation?



Currently here are my attempts at a,b, and c.



a) [itex] S_{1} = E_{1}[/itex] [itex]\cap[/itex] [itex]E_{2}^{'}[/itex] [itex]\cap[/itex][itex]E_{3}^{'}[/itex]



b) [itex] S_{2}[/itex] cannot be identified



c) [itex] S_{6} = E_{3}[/itex] [itex]\cap[/itex] [itex]E_{2}^{'}[/itex] [itex]\cap[/itex][itex]E_{1}^{'}[/itex]





Is this how you correctly write the answer in set notation?



Also with b) I am also unsure of my answer. Would it be correct to say that E1 is true AND not S6?