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

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SUMMARY

The discussion centers on the logical implications of the statement "There are no women engineering students at CU." The user explores set theory concepts, specifically the relationships between the set of women (W) and the set of engineering students (E). The conclusion drawn is that stating all non-women are engineers (W' ⊆ E) is fallacious, as it does not logically follow from the initial premise. The user seeks clarity on the validity of these subset relationships and their implications.

PREREQUISITES
  • Understanding of set theory and subset relationships
  • Familiarity with logical implications in mathematical statements
  • Basic knowledge of complementary sets
  • Experience with mathematical notation and symbols
NEXT STEPS
  • Study the principles of set theory, focusing on subsets and complements
  • Learn about logical fallacies and their identification in mathematical arguments
  • Research the implications of universal statements in set theory
  • Explore resources on mathematical logic and its applications in real-world scenarios
USEFUL FOR

Students of mathematics, particularly those studying set theory, logic enthusiasts, and educators looking to clarify concepts related to logical implications and subset relationships.

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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\subseteqE'

Therefore
W'\subseteqE

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\subseteqE'


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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