Finding a counter-example to an alleged set identity

[ainster31]

Homework Statement

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?

 

[kduna]

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.

 

[ainster31]

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?

 

[johnqwertyful]

The problem states "A" universal set. Not "the" universal set, which wouldn't really make sense.

http://mathworld.wolfram.com/UniversalSet.html

A set fixed within the framework of a theory and consisting of all objects considered in this theory.

 

[kduna]

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}.