Set Operations: C U U' - Solving with a Simple Subset of the Universal Set

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Discussion Overview

The discussion revolves around set operations, specifically the union of a subset and the complement of the universal set. Participants explore the implications of these operations within the context of basic set theory.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant seeks help in determining the result of the operation C U U', where C is a subset of the universal set U.
  • Another participant explains that the complement of the universal set is the empty set, leading to the question of what C union the empty set would yield.
  • Some participants propose that C U U' equals C, but express confusion about the relationship between C and the universal set complement.
  • There is a clarification that if C is a subset of U, it cannot be a subset of U', as they have no elements in common.
  • Participants discuss the implications of set relationships and the use of Venn diagrams for better understanding.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of the universal set and its complement, but there is disagreement regarding the implications of these definitions on the operation C U U'. The discussion remains unresolved as participants explore different interpretations.

Contextual Notes

There are limitations in the discussion regarding the assumptions about set relationships and the definitions of the complement, which may lead to confusion. The specific mathematical steps and reasoning behind the operations are not fully resolved.

hikki_pop
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some help on sets!

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!
 
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That's easy: the "Universal set" is the set of everything (that we are using in sets) and the "complement" (of A) is "all that are not in A". Since everything is in the Universal set, its complement is the empty set.

Now: what is C union the empty set?
 
i think it would be... C U U'={1,2,3,4,5}, right? but... if the set of c is the subset of the universal set, wouldn't that mean that it's also part of the universal set complement??
 
No, it definitely would not. If A is a subset of B (for any set B, not just U), then A has no elements in common with B'. You can see why this is true using a few examples. Also, when you learn to use Venn Diagrams, you'll understand this better.

EDIT : Didn't realize this could be misinterpreted until it was pointed out. Yes, the opening sentence refers to A being a subset of U'.
 
Last edited:
hikki_pop said:
i think it would be... C U U'={1,2,3,4,5}, right? but... if the set of c is the subset of the universal set, wouldn't that mean that it's also part of the universal set complement??

Yes, C U U'= C. But the fact that c is a subset of the universal set specifically means it is NOT a subset of the complement. As I said before the complement of the universal set is the empty set. Gokul43201's "No, it definitely would not" was in reference to that.
 

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