Set Notation for Identifying Substances: Tests 1-3 and Homework Statement Help

[Dommm]

Homework Statement

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

Homework Equations

Let $E_{i}$ denote the event that the i'th test is positive, $i= 1, 2, 3$

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) $S_{1} = E_{1}$ $\cap$ $E_{2}^{'}$ $\cap$$E_{3}^{'}$

b) $S_{2}$ cannot be identified

c) $S_{6} = E_{3}$ $\cap$ $E_{2}^{'}$ $\cap$$E_{1}^{'}$


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?

 

[Dick]

Homework Statement

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

Homework Equations

Let $E_{i}$ denote the event that the i'th test is positive, $i= 1, 2, 3$

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) $S_{1} = E_{1}$ $\cap$ $E_{2}^{'}$ $\cap$$E_{3}^{'}$

b) $S_{2}$ cannot be identified

c) $S_{6} = E_{3}$ $\cap$ $E_{2}^{'}$ $\cap$$E_{1}^{'}$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?

You haven't said what $S_i$ means, but if $S_i=\{i\}$ then a) and c) look ok. For b) substance two is the only one that is true for tests 1 and 3, isn't it?

 

[Dommm]

doh! I see. Thank you :)

How about the notation? Is the way that I represented the answers correct?

 

[Dick]

doh! I see. Thank you :)

How about the notation? Is the way that I represented the answers correct?

I don't know what your class expects, but if you define the sets as you have then the relations you have written are correct.