Simplify Sets: U={1-14} and C={1-5}. Find C union complement of U in easy steps!

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Discussion Overview

The discussion revolves around the mathematical operation involving sets, specifically the union of a subset and the complement of a universal set. Participants explore the implications of different definitions of the universal set and the universe of discourse.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asks for the result of the operation C U U', where U is defined as the universal set {1,2,3,4,5,6,7,8,9,10,11,12,13,14} and C is the subset {1,2,3,4,5}.
  • Another participant suggests that the universe of discourse must be specified, indicating that the result of C U U' could vary based on whether the universe is the natural numbers, integers, or another set.
  • A participant points out that if the universe of discourse is U, then U' would be the empty set, leading to the conclusion that C U U' would simply be {1,2,3,4,5} in that case.
  • One participant emphasizes the variability in how different authors and professors define the universal set and universe of discourse, noting that this can lead to confusion in mathematical discussions.
  • Another participant expresses agreement with the notion that terminology can vary, highlighting the importance of clarifying definitions in mathematical contexts.

Areas of Agreement / Disagreement

Participants express differing views on the definitions of the universal set and universe of discourse, indicating that there is no consensus on how these terms should be applied in this context.

Contextual Notes

There is uncertainty regarding the assumptions about the universe of discourse and how it affects the interpretation of the complement of the universal set.

hikki_pop
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can anyone tell me the answer to this??

if
U (universal set) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14}
C (just a simple subset of the universal set U)= {1,2,3,4,5}

then what would be the answer if:

C U U' ? (subset C union universal set complement)

thanks !

sorry for the double post! please delete this one!
 
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Don't you need to also include your universe of discourse?

If your universe of discourse is the natural numbers then,...

C U U' would be {1,2,3,4,5} U {15,16,17,...}

If your universe of discourse is the integers then,...

C U U' would be {... -3,-2,-1,0} U {1,2,3,4,5} U {15,16,17,...}

For other universes of discourse it could get ugly. :surprise:

Edited to add the following possibility,...

If your universe of discourse is U then U' is the empty set so,...

C U U' would be just be {1,2,3,4,5}
 
Last edited:
Neutron star: the original post said "U (universal set) = 1,2,3,4,5,6,7,8,9,10,11,12,13,14}.

That is the "unverse of discourse".
 
HallsofIvy said:
Neutron star: the original post said "U (universal set) = 1,2,3,4,5,6,7,8,9,10,11,12,13,14}.

That is the "unverse of discourse".
That's normally what I would assume too, but I've found that different people use different notations including college professors and textbook authors. I've seen the term universal set used to refer to a specific set while the author (or professor) continues to treat the problem as though the universe of discourse is still the natural numbers.

I would agree that they are technically incorrect in doing this. But they seem to do it quite often just the same. I've actually confronted a college professor about this once and all I got in return was a lecture on the difference between a universal set and the universe of discourse.

Don't look at me. I'm with you! As far as I'm concerned professors and authors who think there is a difference are wrong. But since its an imperfect universe (no pun intended) I like to cover all my bases. :approve:
 

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