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

[hikki_pop]

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!

 

[HallsofIvy]

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?

 

[hikki_pop]

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??

 

[Gokul43201]

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'.

 

[HallsofIvy]

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.