Question

If the statement shown below is true for all sets C and D, select "true." If it is not true for all sets C and D, select "false." Assume that C≠∅, U≠∅, and C⊂U.

U⊂∅

I don't understand how to go about solving this or showing that it is true of false

Answer 1

So I put that is was false because in the assumption it showed that U≠∅ so that means that U⊂∅ would be false. I was right. But was I right in the way I went about solving the problem?

Answer 2

I was reading before I responded.

U⊂∅

means that the universe set is a subset of the empty set. That is not true.

The other wayh around, ∅⊂U is true as the empty set is a subset of every other set.

Bottom Line: I agree with you on the answer but not on your logic because two sets that are not equal can still be subsets of each other.

It is that the empty set was involved in this that made the statement false to my thinking.

Answer 3

But, I am not saying that the way you went about solving the problem is incorrect because it made sense to you and yielded a correct answer. Set problems are tricky in my opinion.

Answer 4

I agree they are tricky. I am still trying understand how an empty set can be a subset of the universe. My thinking would say that ∅⊂U also means that there isn't anything in the subset {∅} there is still a subset there but there isn't anything in it. I hope that this is right.

Answer 5

{∅} -> This is a set with one element in it. That element is the empty set.

∅ -> This is the empty set. Some people write it like this --> { } to emphasize that it has nothing in it.

{0} is a set with 1 element in it. The set is not the same as the empty set nor is it the same as {∅}.

{∅} = the same as { { } }.