Finding a counter-example to an alleged set identity

  • Thread starter ainster31
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  • #1
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Homework Statement



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Question #2.

Homework Equations





The Attempt at a Solution



I've drawn a venn diagram for the left-hand side and the right-hand side and I can see that they're not equal but how do I provide a counter-example for this? Wouldn't a counter-example require an infinite number of elements?
 
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Answers and Replies

  • #2
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You can make a counter example with a finite number of elements, in fact I made a counterexample with U containing only a couple elements. I'd recommend just making U a set with a couple elements and then try out a couple of subsets A and B until you get something that works. It shouldn't take particularly long.
 
  • #3
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I'd recommend just making U a set with a couple elements

You can do this? I thought U had to contain all the elements possible in Mathematics? Why is it called a universal set then?
 
  • #5
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You can do this? I thought U had to contain all the elements possible in Mathematics? Why is it called a universal set then?

You certainly can do this. The set is not called universal because it contains everything you could possibly think of mathematically. The term universal comes from the fact that we need to know that the sets A and B exist somewhere (in some universe) so that we have some backdrop to perform these set operations in. So we just say that A and B are subsets of some universal set U.

Try letting U = {1, 2, 3}.
 

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