Are All Non-Women Engineers? Investigating the Validity of a Subset Statement

In summary, the conversation discusses statements made about the student body at CU regarding the presence of women engineering students. The conversation delves into the validity of the statements and raises questions about the interpretation of set notation. Overall, the conversation highlights the potential fallacy of concluding that all non-women are engineers based on the given statements.
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blade123
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Homework Statement



Given the following four statements concerning the student body at CU:
...
b) There are no women engineering students at CU
...

Homework Equations



n/a

The Attempt at a Solution



Let W be the set of all women
Let E be the set of all engineering students

W[itex]\subseteq[/itex]E'

Therefore
W'[itex]\subseteq[/itex]E

However I don't know valid the first, and therefore the second statement is. In the book I'm using, it doesn't cover any "not a subset" other than complimentary.

However, to conclude that all non-women are engineers seems fallacious. Or is that the point?

Is is valid to say:

W[itex]\subseteq[/itex]E'


The set of all women are in the set of non-engineering students.

It's not really homework for a class, but is homework style.
 
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FAQ: Are All Non-Women Engineers? Investigating the Validity of a Subset Statement

What is a subset in set theory?

A subset in set theory refers to a set that contains all the elements of another set. In other words, all the elements in the subset are also present in the larger set.

How is a subset denoted?

A subset is denoted by the symbol ⊂, which means "is a subset of". For example, if set A is a subset of set B, it would be written as A ⊂ B.

How is a subset different from a proper subset?

A subset contains all the elements of another set, whereas a proper subset does not contain all the elements of the larger set. In other words, a proper subset is a subset that is not equal to the original set.

How do you determine if one set is a subset of another set?

To determine if one set is a subset of another set, you need to check if all the elements in the first set are also present in the second set. If this is true, then the first set is a subset of the second set.

Can a set be a subset of itself?

Yes, a set can be a subset of itself. This is because all the elements in the original set are also present in itself, meeting the criteria for being a subset.

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