# Need a real life example that satisfies the property?

1. May 10, 2013

### ankitsablok89

I was solving a question which is the following :

Give examples of 3 sets W,X,Y such that W ε X and X ε Y but W doesn't ε Y . I solved the question by taking the following 3 sets:

W = {1,2}
X = { 7 , 8 , W}
Y = { 3 , 4 , X}

looking it from the theory point of you I find that W is not a part of Y but the problem is I cannot come up with an example from real life that satisfies this condition. Kindly help me visualize this.

2. May 10, 2013

### Staff: Mentor

You need some nested set structure.

A human is an elements of the set of all humans, and the set of all humans is an element of the set of all species. A single human is not a species, therefore it is not in the set of all species.

3. May 11, 2013

### ankitsablok89

If human is a set of all humans and the set of all humans belongs to the set of all species is it not the case that the human belongs to the set of all species, representing it via Venn Diagram says that it is but I am not sure what you intend to say is true or not. A good explanation might help

4. May 11, 2013

### Rogerio

class_01 = {Mary, Lucy, John}

John is a student, and class_01 is a set of students.
Is the head of John a student?
Is the head of John a student of class_01?
The head of John is not an element of the class_01.

5. May 11, 2013

### ankitsablok89

I think this is a wrong example, first of all its not clear whether John is an entity in a bigger set or a set itself, also where are the relationships X ε W and W ε Y in the above example, kindly be clear about the example you mentioned.

6. May 11, 2013

### Staff: Mentor

It is both, that is the point of Rogerio's and my example, and it is exactly what you are looking for.

A Venn diagram is logic, not set theory.

humans={Rogerio, you, me, ...}
species={humans, cats, dogs, ...} (neglecting that cats and dogs are actually many different species)
We are not elements of the second set. We are elements of an element of the second set.

7. May 11, 2013

### pwsnafu

In set theory everything is a set. John is a set, which contains head, body, arms, legs.

W = head. X = John. Y = Class.
W is an element of X.
X is an element of Y.
W is not an element of Y.

8. May 11, 2013

### ankitsablok89

Thanks for the replies people I understand the thing exactly now :)